President Francois Hollande feels "great pleasure" over the release, his office said in a statement.
Sudanese security agents launched a search for the man, whose identity has not been revealed, in late March after a Chadian minister said he was being held there.
The man was kidnapped near Goz Beida, in southeastern Chad, on March 23.
Several French and other Western nationals have been kidnapped by jihadist groups in west and central Africa in recent years.
He was freed after 89 days.
Chad is one of France's key African allies in the counter-terror fight, with the capital N'Djamena serving as headquarters for France's Operation Barkhane anti-jihadist force.
Set up in 2014, the force, which counts 4,000 troops, works in five Sahel countries - Chad, Mali, Niger, Mauritania and Burkina Faso - to flush out Al-Qaeda-linked extremists.
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