General manager Vincent Lavenu said the team made the decision, along with full agreement from Geniez, after a team camp last month.
"Alexandre didn't seem to have the fitness and recovery, after having finished the Giro d'Italia in 11th place, that would guarantee the sort of condition he would need to have in order to assume an important role within the team for the Tour de France," Lavenu said. "With a few more days of training and with the French championships under his belt, the decision has proven to be the right one, which is not an easy decision for a top athlete."
Frank was fourth in the recent Swiss road championships behind winner Steve Morabito (Groupama-FDJ), but is confident he is up to the task.
"I had good sensations during the Swiss championships, but that race is still basically a lottery," Frank said. "Even though I'm sorry for Alexandre, I feel lucky to be at the start of the biggest race in the world again with the AG2R La Mondiale team. I hope to help and accompany Romain for as long as possible in the mountains."
Geniez says he realised that, with his current form, he would not be able to do the job of supporting Bardet properly: "So I decided to give up my spot to a rider who could. The Giro, where I took 11th place overall, was long, and even though I have been trying, I have not yet managed to regain the full extent of my fitness.
"I hope to recover quickly and to find the right rhythm for competition. Watching from home, I'll be giving my full support to the team at the Tour."
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The 2018 Tour de France starts on July 9 and concludes on July 29 in Paris. Cyclingnews will have complete live coverage from the race, as well as race analysis, blogs, video highlights and podcasts from the team on the ground.