Opinion polls make independent centrist Emmanuel Macron the favourite.
But the gap separating him from the other top three contenders - Marine Le Pen on the far-right, conservative Francois Fillon and far-leftist Jean-Luc Melenchon - has narrowed.
Any two of the four might qualify on Sunday for the May 7 two-person run-off. Here are the possible scenarios for Sunday's election:
MACRON VS LE PEN
Polls have forecast this run-off scenario as the most likely since early February.
It would represent a seismic shift in France's political landscape, featuring neither of the mainstream parties that have governed the country for decades, and pitting a man who set up his party just a year ago against a woman who wants to take France out of the European Union.
Seeing Le Pen in the second round could un-nerve investors even though they and French voters have had plenty of time to get used to the prospect.
Opinion polls forecast that the 39-year-old pro-EU, centrist Macron would win the contest easily, depriving Le Pen of the chance to become France's first woman president at 48.
A Macron presidency would beg the question can he win a majority in the parliamentary elections that follow in June. A Le Pen victory would be much more of a shock, but for her, much would also hang on the June ballot.
FILLON VS LE PEN
This was, until late January, seen as the most likely outcome. Now Fillon polls in third, or arguably fourth place, because of a nepotism scandal involving his wife.
The 63-year-old has made a modest comeback though, and pollsters see a possible last-minute boost from conservatives who had been put off by the scandal but would eventually balk at putting Macron into the run-off instead of him.
Fillon's margin of victory over Le Pen is seen as the smallest, so investors may find this second-round scenario more chilling than the above pairing.
Fillon denies wrongdoing, but the scandal would likely follow him into the presidency, casting doubts over how easily he can push through his already controversial plans for steep spending cuts. He may, nevertheless, have a smoother run to a parliamentary majority than Macron or Le Pen, given that he has a party structure in his The Republicans grouping.
MACRON VS FILLON
The big surprise here would be Le Pen's failure to make it to the run-off, confounding years of opinion polls. With Melenchon also not in the second round, both anti-EU contenders would be out - likely a relief for investors.
Opinion polls show Macron beating Fillon easily in the second round.
While missing out on the run-off would be certain to create a lot of soul-searching in the FN, experts say Le Pen's grip on the party remains strong despite tensions with her niece Marion Marechal-Le Pen. How the FN fares in the parliamentary elections that follow in June would be crucial.
MELENCHON VS LE PEN
This would be the biggest shock for financial markets, with two populist, anti-EU candidates, to the far-left and far-right of the French political spectrum.
Melenchon's surge in polls in the back of strong performances in TV debates late March and early April is the latest surprise in the topsy-turvy campaign.
While no opinion polls have so far predicted he would make it to the second round, the 65-year-old is now challenging the pollsters' margins of error.
Opinion polls suggest him beating Le Pen in a second-round match. He too, though, would want to overhaul the EU or pull France out. Also like Le Pen, he would likely struggle to attain a majority in parliament to carry out his plans.
MELENCHON VS MACRON
Polls show Macron easily winning such a run-off, which would pit two very different views of France's future and its relationship with Europe against one another.
MELENCHON VS FILLON
This scenario is less likely than all those above because Melenchon and Fillon rank third and fourth in the opinion polls.
If Melenchon did qualify for the run-off, a hypothesis that would have been seen as totally far-fetched just three weeks ago, the former Trotskyist is seen by opinion polls as beating Fillon.
But much could happen in terms of voter support before a second round.
Socialist candidate Benoit Hamon's ratings have plummeted to as low as 8 percent and no pollster sees him qualifying for the second round. Even less likely to figure are the two Trotskyists, three fringe nationalists and a former shepherd-turned-centrist lawmaker who are also candidates.
Another extremely unlikely scenario would be one of the 11 runners attracting 50 percent of the votes in the first round and thereby winning outright.
Opinion polls currently show no candidate getting even half that.