If next month's presidential election turns out as expected, France is heading for confrontation over the disastrous austerity drive now choking the economic life out of the eurozone. As in Britain, the economy is struggling to recover from the crash of 2008, loaded down with bad bank debts and heading for debilitating cuts and tax increases – but with the added burden of being locked into a German-orchestrated treaty that would make an economic stimulus illegal.

Since last month's atrocities in Toulouse, President Nicolas Sarkozy has improved his poll ratings a bit, pandering to xenophobes and Islamophobes and posturing as a security champion. But the most unpopular president in the 53 years of the French fifth republic is still at least six points behind his Socialist rival for the second-round runoff. Barring unforeseen upsets, a post-crisis incumbent is once again expected to be put to the sword and François Hollande elected president in May.

The bland Hollande is very far from the swivel-eyed radical he has been portrayed in the British media. "We opened up the markets to finance and privatisation," he boasted recently of the neoliberal-friendly Socialist governments of the 1990s. And he has backed the "golden" balanced budget rule required by the new fiscal treaty. But he has also promised to renegotiate the treaty, and supports a jobs programme paid for by bank and wealth taxes, along with a 75% tax rate on those earning more than a million euros a year – the stuff of George Osborne's nightmares.

What has transformed the contest has been the dramatic rise of Jean-Luc Mélenchon, former Socialist minister and candidate of the Front de Gauche (Left Front), who has gone from 6% to 15% in a few months to become the pivotal "third man" in the election. He has done so with an unashamedly populist campaign, targeting marginalised working class voters prey to the National Front, inspiring the young and non-voters and using the kind of street language alien to the magic circles of the French political establishment he abandoned.

The result, as the Economist reported, has been a "sensation". Last month Mélenchon called for a "civic insurrection" in front of 100,000 supporters in the Place de la Bastille in Paris. Backed by the communists, he has united almost the entire fractious French left behind him, calling for a cap on incomes over €360,000 a year, the dismantling of Nato, control of the banks, withdrawal from Afghanistan, a referendum on the EU treaty, European "disobedience" and a right for workers to take over plants threatened with closure.

Crucially, he has taken head-on the National Front's Muslim-baiting Marine Le Pen – who he denounced as a "filthy beast spitting hatred" – and overtaken her in the polls, helping to dispel in the process the threat that she might reach the runoff, as her father did in 2002. Even more tellingly, Mélenchon's success has pushed both main candidates to adopt more radical rhetoric on the economy: Hollande's 75% tax was a direct response to the Mélenchon phenomenon, while even Sarkozy now demands the rich pay more and toys with some EU disobedience of his own.

There is of course no read-across between a national French campaign engaging millions and last week's extraordinary election result in Bradford West, which saw George Galloway win a larger increase in the share of the vote than in any byelection (Northern Ireland apart) since 1945, and with more votes than all the other parties put together. But some parallels are still striking.

In both cases a well-known former parliamentarian from the main centre-left party has used a charismatic radical left populism to mobilise alienated voters at the sharp end of austerity against a political elite that has failed to deliver for them for decades.

As is the case with Mélenchon, the metropolitan media so loathe Galloway that – with the exception of the Guardian – they failed even to report the growing tide of support for Respect during the campaign and have been largely unable to make sense of it since, dismissing the result as a one-off based on Galloway's larger than life personality and ability to "play the Muslim card".

It's true that Galloway's record on western-backed wars and occupations in the Muslim world, and his uncompromising defence of the most demonised community in the country, gave him a particular credibility in a constituency with a 37% Muslim population. And the call for withdrawal from Afghanistan is certainly popular with Muslims – though it's also supported by 70% of the entire country.

But the central thrust of Galloway's pitch in Bradford was in fact about cuts, tuition fees, unemployment, poverty and the decline of a city neglected and mismanaged by all the main parties. Respect campaigned as "real Labour" against New Labour, while Galloway declared he wanted to "drag Labour in a progressive direction". And far from dividing communities on ethnic or religious lines, he won majorities in every part of the constituency, including the mainly white areas.

Bradford was a vote against austerity and war, but also against a reviled me-too political establishment, local and national. That alienation has been growing for years, but as cuts are forced through and living standards squeezed further, expect more one-offs whenever the opportunity arises.

Such alienation is common across de-industrialised, deregulated Europe and can also be exploited by the right. It's a common assumption, based on the experience of the 1930s in particular, that the populist right is best placed to exploit the volatility and insecurity of slumps. But both the Mélenchon and Galloway campaigns, among others, are a reminder that the left can set the political pace if it's prepared to give a voice to people's real concerns.

In France, the only real danger of a Sarkozy win is if Hollande is not seen to be offering a genuine alternative. And the stronger the vote for Mélenchon in the election's first round, the more difficult it will be for Hollande to cave in when a clash with Angela Merkel, Brussels and the financial markets comes.

As for Britain, a Mélenchon or Bradford-style platform could not of course make up a winning national strategy. But both point to a yawning unrepresented political space. Either Ed Miliband is bolder in moving Labour away from a discredited inheritance and giving a powerful voice to what he calls its "battered base" – or others will fill it as the costs of crisis bite deeper.

Twitter: @SeumasMilne

• This article was amended on 4 April 2012. The original said, incorrectly, that in Bradford West, George Galloway won a larger share of the vote than in any byelection since 1945. In fact he won a larger increase in the share of the vote than in any byelection (Northern Ireland apart) since 1945. This has been corrected