Analysts say markets would do best if one of the centrist candidates — former Economy Minister Emmanuel Macron or mainstream conservative Francois Fillon — takes more than 50 percent of the vote, ending the need for a runoff on May 7. But there's very little chance of that happening.
Next best for markets would be that both of those candidates are the choices heading into the second vote. That could ignite a global risk rally, sending equities higher and pushing the U.S. indexes back near all-time highs. But the odds are slim for that as well.
There is little chance such a fractious election would end with a clear-cut outcome, but there are small odds of a worst-case scenario in which the first round could usher in a race between the two candidates markets fear most — the far-right Marine Le Pen and far-left Jean-Luc Melenchon. While there's not a high probability, there could be a panicky sell-off, sending stocks sharply lower and safe haven assets, like Treasurys and gold, higher.
Right now, it looks like it will end up being Le Pen and Macron battling it out in the second round with the latter winning, analysts say.
"There's not a happy market solution," with that outcome, said Marc Chandler, head of foreign exchange strategy at Brown Brothers Harriman.
"All the polls show Le Pen and Macron in the top two, and the polls may differ on how close it is. Investors seem to be going into it very calm." Chandler said that's the scenario he expects, and it's likely the euro would rally on a Le Pen-Macron race.
Citigroup analysts expect Macron to ultimately win, with a 35 percent probability, and they say he would go into the race with a good margin against all other candidates in the second round. Fillon would be second most likely, with a 30 percent probability, and Le Pen's odds are about 25 percent. The analysts see a small 10 percent probability for Melenchon.
"That gives a 65 percent likelihood of a risk-on, pro-EU final outcome and 35 percent probability for a risk-off, anti-EU outcome. A market-benign outcome still seems most likely but there is a meaningful risk that something more worrying happens," the Citi analysts wrote.
They say French and European equities would go down as much as 10 percent on a win by Le Pen or Melenchon, and U.S. equities would outperform. This outcome could also drive the euro to parity against the dollar. They say a win by either Macron or Fillon, on the other hand, could lead to 10 to 20 percent upside for European stocks by year-end.
But Bank of America Merrill Lynch believes a victory by Fillon in the first round would not be a positive for markets, since he could potentially lose to one of the extremist candidates in the second round.
"There are more negative than neutral or positive scenarios," said Mark Cabana, head of U.S. short rate strategy at BofA.
"If Macron does make it to the second round that should take some of the tensions out of markets. As long as he makes it, some of these other very negative scenarios go away."
If Fillon is pitted against one of the extremists, markets may take it badly. "Our European team thinks we have French spreads widen out pretty noticeably in that type of scenario and we could see the 10-year [Treasury] continue to rally," he said.
"Markets seem to be behaving in a way suggesting there's no clear outcome priced. Therefore, we're expecting if Macron gets in, he probably beats whichever extremist would get on for the other spot, and that would be a positive market reaction. U.S. equities, risk assets around the world would go higher. Commodities, emerging markets, Europe, obviously would all go higher," said Paul Christopher, chief international investment strategist at Wells Fargo Investment Institute.
"If the ticket ends up being Le Pen, Melenchon, that would be a nightmare scenario. It's not really a Frexit scenario either. It's just the president cycle. I doubt you're going to get a National Assembly vote in June that would give a majority to either of them," said Christopher. The French parliament is up for election in June.
Le Pen has campaigned on a promise to take France off the euro, but analysts say she would need parliament to back her and that is unlikely. Melenchon would like to renegotiate France's relationship with the European Union, and if it fails, he would seek to have France leave the EU.
A fan of Venezuela's Hugo Chavez, Melenchon would like to tax individuals who earn 400,000 euros ($430,000) or more at a tax rate of 100 percent.
Christopher said it would be a worry if either of those candidates were to do well, and looked able to win the next round. "My real concern is an extremist does two things. It shows populism hasn't faded in Europe and it means that reforms that were so painfully worked through in this last government could be rolled back. Those reforms really need to gain some further momentum so the economy can grow faster," he said.
Work rules are one of the areas where there have been reforms. Christopher said the French economy has been stifled by tough firing rules, which encourage French companies to hire temps over permanent employees, and by the high barriers to entry in such fields as medicine.
Analysts say the uncertainty could hang over the market for weeks, between Sunday and the run off, and then between the run off and parliamentary elections, depending on who wins.
"It's that unknown and then the very important fact that there's populism. We wanted to close our eyes and pretend it's going to go away. For it to continue from Brexit, to the U.S. and back to France again, it's a sign that Western democracies have a big problem — inequality in income and noninclusive economic growth. You have to sort out the uncertainty. If one of the extremists is going to be president, what is the national assembly going to be like?" said Christopher.
He said victories by either would create more concern about Italy's government being able to hold ground against Italy's Five Star Movement. A win by Fillon or Macron would bring on a global rally.
"That would be a huge relief if you could have a mainstream party suddenly claim a victory in a major country in Europe at a time when everyone is worried about populism," said Christopher.
Watch: French voters head to polls on Sunday