Socialist Benoit Hamon and Jean-Luc Melenchon, a former member of the Socialist Party who is supported by the Communists, both announced over the weekend that they are staying in the race.
Despite opinion polls suggesting that neither one has a chance of reaching the second round, they have shown little appetite for joining forces since Hamon won the Socialist primary last month, the Associated Press reported.
Speaking on France Inter radio on Monday, Hamon said: "I would have preferred a union around my candidacy."
Melenchon issued a statement saying they could not put aside their differences but agreed on a "mutual respect code" throughout their campaigns.