A man claiming to represent Corsican separatists has admitted responsibility for two bomb attacks in Nice and another in Corsica.
Many of those injured in Nice were hit by flying glass
The Nice attacks, early on Sunday, targeted public buildings, injuring 16 people.
The Corsica blast came later in the day at a warehouse near Bastia airport.
The attacks appear to confirm fears that an upsurge in separatist violence might follow the rejection of limited autonomy for the Mediterranean island in a referendum held earlier this month.
The caller claimed to represent the banned FLNC (Corsican National Liberation Front) which has officially been observing a truce for the past seven months.
Tension on the island has been increased by the arrest of militant suspect Yvan Colonna and the jailing of eight men for the murder of Corsica's prefect in 1998.
French Interior Minister Nicolas Sarkozy attacked the "mafia-style" path the bombers were taking.
"The perpetrators will be tracked down...and they will be punished," Mr Sarkozy said.
Militant separatists have been campaigning for three decades to break away from France.
One of their main tactics has been the bombing of holiday homes owned by non-Corsicans.
Another villa, owned by people from mainland France, was bombed late on Sunday, police say.
The Nice attacks targeted the treasury and customs buildings.