Normally your contract is transferred to your new home.
Tell your insurer to have the new address on your contract, he will check with you to know what is the size of your new home, what are the new elements to achieve and what price you will pay!
From a legal point of view, you must notify your insurer by sending a « lettre recommandée avec accusé de réception » within 15 days after your change of address. In practice, you can always go to your insurance and inform them of this change. If he immediately change the address and gives you a new certificate of insurance, everything is ok.
If when you move you want to change insurance, you must send a letter of notice with acknowledgement of receipt « lettre de préavis en recommandé avec accusé de réception » in the notice period defined by your contract « délai de préavis ».