The deeply unpopular Hollande has yet to announce whether he will run for a second term next year, but is widely expected to be a candidate.
In a speech on terrorism and democracy in Paris he defended the country's Muslim minority following a vitriolic debate on the banning of the Islamic burkini swimsuit.
"Nothing in the idea of secularism opposes the practice of Islam in France, provided it respects the law," Hollande said.
Mayors in around 30 French towns this summer cited the country's century-old secular laws in banning head-to-toe swimwear on their beaches, unleashing a furore.
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Several of the towns later revoked the bans after France's highest administrative court ruled they were a "serious" violation of basic freedoms.
Hollande rejected calls by conservatives, including his arch-rival, former president Nicolas Sarkozy, for a ban on the burkini, saying it would be "unconstitutional".
As to whether Islam can co-exist with a secular French state, like Christianity and Judaism do, he insisted: "My answer is yes, certainly."