France has the exact same rule as Italy, 1 star for every 10 national titles. However, the application of this rule isn't as black and white as the rule itself.
Saint-Etienne was the first French club to reach 10 national titles in 1981, an achievement that is celebrated with a big star on their crest with French flag colors. Olympique Marseille is the only other French club with a star on it's crest but it is not for 10 national titles (they have 9), but for their 1993 UCL championship. To this day OM is the only team from France to have won the Champions League so they sport the star very proudly. It will be interesting to see what the club decides to do when they eventually win their 10th Ligue 1 title as well.
PSG's recent investment and success has led the club to surpass the 10 title mark, however they decided not to add the star on their crest. Even though it was never publicly admitted, it is strongly believed that the PSG is leaving the honor to the Champions League title which everyone knows is the ultimate goal.
Interestingly, Nantes FC had 8 stars inside their crest representing their 8 national titles. Those stars have since been removed after a rebranding of their crest so we'll have to wait for 2 more Ligue 1 titles to see stars on Nantes's crest again.