The 29-year-old Fritz has been a regular starter for France since coach Philippe Saint-Andre took charge last year and has 34 caps to his name.
"Florian was involved in an accident while driving his motorbike and has either broken or dislocated his arm," Toulouse manager Guy Noves told a news conference.
"He will certainly be out for two months."
France, who finished bottom of the Six Nations in March, host England on February 1 and Italy the following weekend. They visit Wales on February 21, with Fritz likely to miss these first three matches.