It's been 10 years since Franz Ferdinand's rise to fame, two since the group were rumoured to have split, yet their new album is tipped as the sound of the summer. Craig McLean asks the group how it all went so right, then wrong, then right again

Last summer's hit novel Gone Girl opens with a scene set in the trendy early noughties magazine circles of Brooklyn. "The party is being thrown by one of Carmen's good friends who writes about movies…" begins the American author Gillian Flynn, throwing the protagonists into "a whoosh of body heat and writerness… black-framed glasses and mops of hair… black wool pea-coats flopped all across the couch." A German poster for The Getaway covers "one paint-cracked wall". Franz Ferdinand is "on the stereo". The song playing is "Take Me Out".

I read this passage out loud to Alex Kapranos, singer with Franz Ferdinand. At first he says nothing, so I explain the subtext; how the group he formed in Glasgow in 2002 embodied a du jour cool. "Yeah, yeah, yeah," he says quickly, frowning, looking pained. We are in deepest, greenest Dumfriesshire, in the conservatory of a large, slightly ramshackle Victorian house the musician bought in 2004 as a bolthole, discussing Right Thoughts, Right Words, Right Action – Franz Ferdinand's fourth album, and their first since 2009. It is a bright energetic record, but one which has been clawed from a slough of despair.

Kapranos wasn't aware of the Gone Girl namecheck, despite the thriller's bestseller status. Or perhaps it was because of it: Kapranos is an English graduate, one-time divinity student; the sort who references Soviet-era magic realists and Dadaism in his work. Of all the territories in which Franz Ferdinand had immediate soaraway success, the US proved the most burdensome. There are moments he would rather forget, such as the band's boss at their label in America flying to see them play for the first time in Boston – via private jet. "And I'm thinking, 'What the hell are we getting into here?'" Kapranos recalls, exasperated even now. Having been unable to stay with their UK indie label Domino in the US, the foursome were signed to a major. "[Domino] only had three staff in America and couldn't physically deal with the amount of records that we were selling," Kapranos explains.

That was then: the band backstage at the ICA London in 2003. Photograph: Danny Clifford/Hottwire.net/WENN

Corporate music biz America proved to be a world of largesse and excess. Things worsened for the band when their label was taken to court, accused of offering bribes to DJs to play the hot new releases by their hot new acts. Franz Ferdinand's name was read out as part of the prosecution case. "And I was like, 'Fucking hell, here we are in court on some payola charge," Kapranos says. "It was exactly the opposite of what I wanted to be as a band." He gives a grim nod. "They pushed us in a way that didn't feel natural. I shouldn't complain too much – we sold lots and lots of records. But I think the way it accelerated so quickly was probably quite damaging for us." In many ways it was the beginning of the end for Franz Ferdinand.

I first met the band 10 years ago, when Kapranos, Nick McCarthy (guitar, keyboards), Bob Hardy (bass) and Paul Thomson (drums) were playing Reading Festival's New Bands tent. They were yet to release a single and had an afternoon slot, immediately after another bunch of hopefuls called Razorlight. They were sensational: a pop band with spikes; a rock band with jump-around adrenaline; an indie band with club-friendly synthesiser lines. They were a bit camp. I spoke to them backstage afterwards. "Fantastic crowd today, so full of energy, we were getting so much back off them," the well-spoken Kapranos beamed in an accent that betrayed both a childhood in Sunderland and an adulthood in Glasgow. When I asked what this brand new band sounded like, the singer shot back: "Music for girls to dance to."

Five months later, "Take Me Out", their second single, entered the UK charts at No 2. By spring 2004 their debut album had sold a hefty 300,000 copies in two months; it would go on to sell 1.1m copies in America alone. That September it won the Mercury Music Prize and in February 2005 Franz Ferdinand took home two Brit Awards, for Best British Group and Best British Rock Act. Their second album, You Could Have It So Much Better, went platinum in the UK, gold in the US. Having watched them graduate from sticky Glasgow squats to festival headline slots, I found myself travelling to interview the band a handful of times, everywhere from Germany to Poland to America to Australia.

Three weeks earlier than my visit to Kapranos's house, I met the rest of the band at McCarthy's studio in Hackney, the Sausage Factory, a cupboard-sized space in which the guitarist has crammed a junk-shop's worth of arcane musical kit. McCarthy, born in Blackpool and now aged 38, is first joined by Paul Thomson, 36, this so-called Scottish band's sole actual Scotsman. They tell me the album – a short, sharp, whipsmart disco-rock record – was recorded in fits and starts in studios across London, Scotland and Sweden in the past year. Both pronounce themselves pleased with how they made their new album. It has no single producer, but saw friends (including Hot Chip and Björn Yttling of Peter Björn & John) occasionally managing the studio controls.

It's a long way from 2009's Tonight, which sounded clenched and felt tired. According to Thomson, a period "decompressing" was required in the wake of the two years spent touring their third album. "[Afterwards] I just came down heavily with depression, I think," says McCarthy. "I just thought, 'Eurrgh, can't play music any more.' Couldn't stand it. We'd sucked ourselves dry."

It was, they admit, partly their own fault. Tour America for the fourth time in a year? Of course! Record a song for David Mackenzie's 2007 film Hallam Foe? No problem. "Perform" (via clever lookalikes) in a Dior ad starring Marion Cotillard? Bien sûr… Franz Ferdinand jumped at the bewildering array of opportunities that came their way. It was no surprise. "Before this I had 10 years of doing fuck all!" Thomson chuckles ruefully. Having found success in their mid-to-late 20s (in fact, Kapranos was four years older than he claimed), in new-band terms they were ancient. So they were hungry. "We were making up for lost time," says the drummer. Hardy, the Bradford-born bass player, 33, remembers thinking this frantic pace was "normal" for new bands. "I didn't," Kapranos adds with a thin smile. Did the fun go out of it for the frontman? "Undeniably. It went out when I felt I was working to someone else's schedule or deadline. I'm not naturally the kind of person who works well under those conditions. In fact, my whole adult life before that point, if I'd been in a job where I felt I was under pressure, I would usually just jack in the job. And suddenly I couldn't do that any more. But maybe…" the singer sighs quietly, "Maybe, that's what we did after the third record."

When I meet Kapranos again in Dumfriesshire the following month I ask him whether he is saying that Franz Ferdinand split up after finishing touring Tonight. He ums and ahs while fiddling with a jar of homemade plum jam. "I met up with Bob in Orkney about two years ago," he finally offered me, describing how they chose the northerly Scottish islands because they were "neutral territory" (neither had been there before). "I wanted to split the band up, because in my head it felt like one of those jobs… the ones I had to jack in. I didn't like the routine and the obligations. And whether those obligations lay with my contemporaries, my peers, my record label, the fans, the audiences – or maybe myself… I felt…" He stutters awkwardly. "It was time to, erm, stop that."

There were various factors at play. The food column he wrote for the Guardian "for fun" during a world tour morphed into a book. It then mutated into something else entirely for the serious-minded fortysomething. "It contributed to creating a comic character version of yourself. It happened the other day – I was doing a phone interview with an Australian newspaper and they began by saying, 'I've got my mouth full of food this morning and I'm thinking of you, Alex! What you do think of beef jerky?' I'm like, 'Oh God, is this it? Is this my life?'" he wails.

Franz Ferdinand photographed for the Observer in Hackney. Photograph: Julian Broad

Kapranos was "incredibly miserable" during the making of Tonight, also for other, personal reasons he won't discuss. But it seems reasonable to guess that one was the end of his relationship with Eleanor Friedberger, of US brother-sister indie duo the Fiery Furnaces. In Dumfriesshire he politely declines to say anything of his current girlfriend, but later introduces me to a slight, blonde twentysomething with whom he's about to spend the afternoon dinghying down a local river.

Kapranos can be a brilliant, charismatic frontman, a great conversationalist – he radiates cheerful gratitude that I have made the effort to travel to his remote rural home. "I'm not going to get to enjoy this for much longer this summer," he shrugs, staring down the barrel of a weeklong Tokyo-LA-New York-London interview schedule, then heaps more besides. But he is also a heavier, more preoccupied presence than the exuberant, eager chap I met a decade ago.

Still, the comeback album radiates buzzy confidence. It is certainly the best since their groundbreaking debut, and pre-release noise about it is healthy; their social media stats have recently been boosted to 1.4m Facebook likes. They've also gone back to snagging high-profile gigs: in New York last month they streamed a performance of the entire album on the set of David Letterman's chat show. This summer their labelmates Arctic Monkeys, also returning with a new album, are the only British band generating similar levels of excitement.

But Kapranos seems resoundingly relieved by the likelihood that decade-old Franz Ferdinand cannot be the hipsters' new band of choice any more. He is much more energised by rediscovering the founding principles of which he and Hardy reminded themselves during their Orkney crisis summit: Franz Ferdinand should be "odd", and "quirky". Success, though, and repetition, and those obligations, had "shaved off" those qualities. "But when we came to making the new album, we decided that oddness was just us!" He beams. "And we should enjoy that: it should be at the heart of our existence if we want to continue."

My interviews were bookended with two concerts: in April, I saw them perform at California's three-day Coachella festival. They played in a packed tent on the middle evening, before New Order, and it was proper Saturday night fever, the band bristling with grinning exuberance and the crowd responding by dancing wildly. When they segued into a scratchy-guitar version of Donna Summer's "I Feel Love" it was clear that Daft Punk aren't the only postmillennial arrivistes making disco-hay in 2013. The mash-up was both wonky and inspired; a piece with both old and new Franz Ferdinand.

Three months later, they play a secret show in the back room of a tiny pub in Dalston, east London. The show is running late after some shambolic milling about by the band. There are 500-odd fans stuck outside, unable to get in. Kapranos, McCarthy, Hardy and Thomson finally amble through the crowd, then drift onstage. They are all smiles and bashful waves. Clearly, they are following no one's schedule but their own. Just like the good old days.

Right Thoughts, Right Words, Right Action is released on 28 August