The sprinter, who was targeting stage wins and possibly the green jersey for the points classification, was caught in a crash with three team mates and several other riders 18km into the 189.5km ride from Arras.
Bouhanni was the only one who could not resume racing.
"He was taken to a hospital for checks on his ribs, elbow and wrist," his Cofidis sports director Didier Rous said.
Bouhanni had sustained bruised ribs in a crash at the French national championships 10 days ago, only confirming his participation in the Tour at the last minute.
The 24-year-old has three Giro d'Italia and two Vuelta stage wins to his name.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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