When to subscribe to Direct Assurance for a smooth insurance termination

My car contract with Eurofil will end on September 31 and I would like to go to Direct Assurance for the 100€ reimbursed, only as I am still within 1 year, I would like to know when I have to subscribe to Direct Assurance so that they can charge of the termination with my current insurance without them charging me for 2023/2024.

Thanks in advance