Anelka, who has started up front in the two warm-up games France have played so far, escaped unhurt after losing his balance on a slippery road and falling at the end of a 50-minute ride on the spectacular volcanic island.
In an effort to make his team bond, France coach Raymond Domenech has organised all sorts of group activities since the start of their preparations, including a hike up a glacier in the French Alps and a dune buggy race.
The coach's latest idea was a bike ride on Reunion, where the players landed on Tuesday from Tunisia.
Some 100 fans stood in the rain at the ride's starting point and cheered on the players, who waved and smiled but did not stop to sign autographs or talk to the media.
All the players participated except number two goalkeeper Steve Mandanda, who stayed at the hotel but had "nothing serious", according to a team spokesman.
After the ride, the team returned to their luxury hotel, overlooking a beach just outside St Pierre, the island's second largest city.
