The first hurdle for running is to get "sponsorship" from at least 500 elected officials: mayors, regional councilors, senators... This being France, the country with 36,000 communes and as many mayors (there are even Wiki pages for communes under 10 people and even some with no population), it leaves quite a number of options. Some candidates couldn't enough signatures and won't be running.

For this election, both "traditional" parties, the PS and LR (formerly UMP) have nominated their candidates by running primaries: the results were not quite what the pundits were expecting, because François Fillon won for LR in November and Benoit Hamon, a opponent to F.Hollande, won the PS primaries in January.
Fillon, one of the most conservative politicians on the rigth wing side, and a so-called "Thatcherite", has been plagued by the Penelopegate and other financial scandals and is now under formal criminal investigation. Yet he refused to pull out of the race, paying the price by sinking in the polls.

Hamon, decidely on the left of Hollande and Valls, is also sliding in the polls: one of the reasons is that many of his fellow PS members are more or less openly supporting E.Macron.

Speaking of polls, it looks like, for the first time since the advent of the Fifth Republic, the second round won't feature  any candidate from the PS nor the main right wing party LR (or UMP or RPR or whatever...): instead, it is expected that Marine Le Pen, the extreme right FN leader will "win" the first round. Of course, being ahead in the first round doesn't win you jack all, except a spot for the second round.

The second front-runner in the polls is Emmanuel Macron: Adviser to Hollande at the Elysée palace, then Minister of Economy  in the Manuel Valls cabinet, Macron has founded his own party "En Marche"  (On the move) a year ago after leaving the government. His program is mostly centrist neo-lib (he received the support of François Bayrou). A relative newcomer, outside of the traditional political party system, Macron quickly became the darling of the French media. For a couple of weeks now, the polls put him at the same level as Le Pen for the first round and a decisive winner in the second round.

Jean-Luc Mélenchon is the fifth "major" candidate (by "major", I mean: "polling above 10%"). A former Minister of Education in the early aughties, in the Lionel Jospin cabinet, and a former member of the PS which he left in 2008 to create the Parti de Gauche, he is currently polling ahead of Hamon.

To round up the list, we have six "little" candidates who are polling less than 5% (and for most, under a single percent): Nicolas Dupont-Aignan (Debout la France ), Nathalie Artaud (Lutte Ouvrière, a trotskyst party), Philippe Poutou (New Anticapitalist Party, another trotskyst party), François Asselineau, Jean Lassalle and Jacques Cheminade.

Again, all polls today do predict a second round with Macron facing Le Pen (and the former trouncing the latter); then again, polls have been shown to fail to predict the actual results quite a number of times over the past year, so we'll see.

In any case, it is most likely that the next president won't be from neither the PS not the LR party. This is unusual, since they form the two main blocks at the French National Assembly. As I wrote five years ago, the parliamentary elections follow the presidential ones since 2002 and the trend has always been for the voters to give the newly elected president a majority in parliament.

This will create a challenge for either Macron or Le Pen: what will the new majority look like? Who will support the new president?

In the case of Macron, most of the PS plus the MoDeM and other centrists would probably support him. For Le Pen, if is still not very likely that the FN would single handedly win a majority of the seats: they would probably have to seek an alliance with the most conservative elements of the right wing LR.

In any case, these two elections won't be anything like France has known for a half century. Interesting times...