At 9pm, as the street lights glinted off the river Seine beyond Notre Dame cathedral, by the Pont Marie bridge, Yan, 37, was neatly laying out his cardboard boxes for the night in front of a chic sofa-bed shop. A dozen people were already climbing into sleeping bags nearby, an elderly woman was sorting clothes, a man in his 60s was wrapped in a duvet reading a book as the last well-heeled commuters hurried past from the metro. Yan, a Polish butcher, trained in charcuterie, just wanted a job in his trade. "But you can't work with food while you're sleeping rough, it just wouldn't feel hygienic …" he muttered. He had been sleeping rough in Paris for three years, occasionally doing agricultural work outside the city. With the weather not yet plunging to freezing, he felt OK inside two sleeping bags on a bed of cardboard on the concrete. "When it gets colder, we'll go down into underground car parks to sleep. Not the metro, because, with the constant noise and activity, you can't get to sleep before 1am, then you're up again at five. Here, I'll shut my eyes at 10 or 11pm, I'll be gone by seven."

Beside him, Igor, 50, an unemployed Slovakian painter and decorator, remembered sleeping in offices he once worked on. Now he too just wants a job. Do the police bother them? "No, they just patrol at around midnight, have a quick look to check we're all alive."

At the Socialist-run Paris city hall nearby, where election fever is hotting up before next spring, some would argue it's better to be poor in Paris than a lot of other places, saying levels of social aid in the capital are high. But, years after French presidential candidates of both left and right (the Socialist Lionel Jospin, then the rightwing Nicolas Sarkozy) promised that no more people would ever need to sleep rough, the number on cardboard boxes in the street is rising. Campaigners warn that successive French governments have failed to solve not only homelessness but a wider housing crisis. With no clear regular statistics collected, it's impossible to prove what some Parisians believe on their early morning commute past sleeping bags in sandpits in children's parks, mattresses in doorways, sometimes women and children on the pavements: that there are more people sleeping rough in their city than other big European capitals. The French national statistics office warned of a 50% increase in homelessness in France from 2001 to 2012, including a rise in foreigners and women. They calculated 141,500 homeless across France at the start of last year, but charities add hundreds of thousands more at risk and in precarious housing situations.

There's a centuries-long history of people being down and out in Paris, a city with a tradition of transient populations and now more European migrants, said Julien Damon, a sociologist at Sciences Po university. "Paris is seen as an extremely tolerant city and generous in its offer of aid and social protection. It's perhaps the EU city that spends most in terms of public policy on shelter and these issues." He said homelessness was less stigmatised in France. "In London you can't sleep in a tent and stay in the same place all day. In Paris, you can. There's no criminalisation of begging." But if Paris homelessness is perhaps tolerated more than in London and Berlin, that did not mean the problem was being solved by successive governments.

Polls show that French people are sympathetic to the homeless. In European surveys, the French are the nationality most likely to view homelessness as the unfortunate result of financial crisis, unemployment and housing crises and the least likely to blame the individual for personal reasons such as drugs or alcohol. A 2009 poll found that a staggering 56% of French people felt they could one day be homeless themselves, 75% felt "solidarity" with rough sleepers.

The past decade has seen successive protests, such as organised tent cities, in Paris to highlight the plight of the homeless.

Others make their own gestures. Joël Catherin, a young lawyer who began writing quirky cardboard signs for the homeless people in his posh Paris neighbourhood, in turn inspired a short film by Bernard Tanguy. In his flat, Catherin showed me boxes full of hundreds of tattered cardboard signs he had drawn. In Paris, the felt-tipped signs reading "I'm hungry" beside a paper cup for coins are a regular fixture for people sitting on street corners. Catherin had noticed an elderly Romanian woman, Ioana, sleeping rough in his neighbourhood near the Madeleine district with a similar sign. One winter night, angered by the cold and the homelessness problem, he made her a new sign: "I could be your grandmother." It worked, money fell into the pot, people started noticing. He was soon drawing up signs for other homeless people he befriended – comments on politics, football, jokes. From a reference to the FT magazine, "How to Spend it?" to "Sale, end of line", "All we need is love, 1 euro". Locals, social media and the French press began searching out these mysterious, odd and unsettling subtitles of the cityscape.

"Humans don't need subtitles," Catherin said. "It's more that, through the words on the cardboard, passersby looked at these people differently and realised they were human beings. It wasn't about money, it was about changing the way people view others."

"Sometimes it felt as if these homeless people were like human furniture. People passed them while putting their bottles in the bottle-bank for recycling, but didn't think of them as human," he said. The thing about the now infamous sign, 'I could be your grandmother', he felt, was that "it made people go and speak to her, show some sympathy. It became part of our neighbourhood."