Lavillenie (35) like Collet (23) stopped at 5.75m, a bar they both ended up crossing on the last try, but the 2012 Olympic champion had only passed 5.60m on his third attempt earlier in the contest.
Both had passed the minima for the Eugene Worlds, set at 5.80 m, before the Norman competition.
The pole vaulter from Grenoble currently has the best French performance of the season, with 5.82 m, one centimeter ahead of Lavillenie.
The latter's younger brother, Valentin, was evacuated on a stretcher after slashing his leg when he fell close to the post on his last try at 5.70 m.
Collet, who is preparing to participate in his first World Championships and first European Championships for seniors this summer, had already been crowned French indoor champion this winter.
© 2022 AFP