One of the fiercest campaigns is being conducted in Lille, which to Britons may mostly be known as the place where the Channel Tunnel train stops before reaching Paris. Looked at from the capital, Lille is the main city in the north, but for the people of the city itself, it is the centre of the world, possessing much the same fierce provincialism as Manchester or Leeds. Its mayoral campaign - the contest that will determine who runs Lille for the next six years - reflects all these tensions.
With a population of 172,000, Lille has several distinct faces. If you arrive at the new Eurolille station - the one used by the Eurostar express - it presents a contrast between 21st-century magnificence and urban decay.
If you come through the old Lille-Flandres station, 200 yards away, you arrive in a finished city, with Victorian-style architecture. But sale boards and "reduced" signs suggest the recession is still unconquered.
If you take the bus or the metro to the south, or the new tramway to the north and east, you find a third Lille. The prevailing colour of passengers is black and brown, and you are quickly into sprawling grey suburbs, with veiled women and the men hanging around gloomy cafes. The work - coal, steel and textiles - that brought so many to the north-east, is in decline.
The future is said to be in finance and services, but these are not sectors that help immigrant manual workers in the suburbs, and they have votes.
The right's candidate, the highly personable Alex Turk, is not a member of either of the two main parties of the right, the RPR or the UDF. He left the RPR when they proposed nominating the new Prime Minister, Alain Juppe, as mayor of Lille, and became an independent. Mr Juppe found himself a more reliable berth in Bordeaux, and Mr Turk was free to lead the challenge to the left in Lille.
His 59-member council list is up against the impressive, and entrenched, party machine of the left, headed by Pierre Mauroy, 66, who has not only been mayor for the past 12 years, but is also a former Socialist prime minister (under President Mitterrand), and one of the party's grandees .
Mr Mauroy's disadvantage is that he represents the status quo. From the outside, that may not look at all bad - Lille has clearly had money poured into it over the years of Socialist government. But people are amazed to hear that from across the Channel, the city is seen as a success. Eurolille epitomises many of their doubts: locals see it as shifting the focus of the city. The old centre seems far from dead, but people feel the risk.
Their other complaint, on which Mr Turk is capitalising, is the amount of local taxes people think is going into grandiose projects like Eurolille. Much of the money has actually come from central government and EU funds; many people, however, feel that it would be better spent sprucing up the suburbs and improving local services.
Mr Turk says he wants to bring government closer to the people and he offers a multiplicity of ideas, from redesigning housing estates to reintroducing mounted police. Mr Mauroy and his team are campaigning on their record - it was he who lobbied to have the tunnel trains stop there. But, after the election of Jacques Chirac to the presidency, he recognises that the mood is for change.
With that in mind, perhaps, Mr Mauroy has proposed as his deputy Martine Aubry, a budding prime minister if the Socialists regain national power. Ms Aubry has not gone down well everywhere in Lille. "A caviar socialist, parachuted in from Paris . Not one of us northerners," people grumble.
The first round next Sunday will show whether Ms Aubry can help retain Lille, or whether the future is with Mr Turk's brand of Chiracism and anti-politics.