When I did this with several friends, we flew Pisa to Paris, had an overnight layover, and continued to Los Angeles the next morning. We all checked our luggage through to LAX at Pisa, and just took carryon bags into Paris for the night. It was no trouble, and our checked bags arrived with us at LAX the next day.

Checking the bags through was a lucky decision--we arrived in Paris on day 1 of the big strike, and our status as connecting passengers with checked bags got us onto our original flight to Los Angeles the next morning. Lots of other passengers were stuck in the chaos in Paris.