You can absolutely change insurance as long as you follow the terms of your contract. Most of the time, insurance companies are tacit agreement "reconduction tacite" which means automatic.
It's very convenient as every year it's your assurance responsability to send your new insurance certificate (yet to sign, place on the windshield and keep the other part always on you with the carte grise "Papiers du véhicule"). But, if you want to change insurance you have to remember to send a letter of notice with acknowledgement of receipt « envoyer une lettre de préavis » en « recommandé avec accusé de réception » 3 months before the expiration of your contract (renewal).
Beware, if you are late (1 month's notice only for example) your insurance may deny you this notice and make you pay 1 year more.
Your new insurance will request a "avis de situation" or « relevé de situation ». You must request this document to your old insurance. This paper will be used to establish your new « côtisation » (what is your situation regarding "bonus" « malus » and how much you will pay ?).