No, France should not rejoin NATO's integrated military command, because France is better off without being confined to the restrictions of NATO's integrated military command. France has a strong military, and with NATO, it would often be committed to sending troops where it might not want to. France would also be a major financial contributor, and it might not want to be.
No, France should not rejoin NATO's integrated military command, because in the past, France's political interests have not always coincided completely with NATO's. France is able to work with the United States on issues of military security without being a part of NATO's military command. Protecting sovereignty is equally important to participating in military actions that involve many nations.