Originally Posted by f0zzyNUE

you can also go to the service desk in the lounge and let you rebook to the next possible flight to PRG - no matter which airline. They are obliged to rebook you onto the next available flight (and that must not be a flight on AF or SkyTeam). The options in the app or the website usually only show AF/KL or other SkyTeam flights.

We had a similar issue with KLM - we needed to go to BUD from NUE via AMS. One night in BUD to catch our OS flight from BUD to VIE and NRT (separate ticekt) departing 11:20 next morning.
Our flight from NUE to AMS was delayed and while we were inflight to AMS we were proactively rebooked to the KL flight next morning that arrived in BUD at 11:00. Unfortunately there was no other flights bringing us to BUD other than an early next morning connection via VIE - that flight arrived in BUD at 10:40. So our only chance to get our flight to the long awaited Japan trip was to take the risk and fly via VIA and make a direct turnaround.

The guy in the KLM lounge service desk took a long time to get what we were about to do. First he said that we were already booked on the next available flight to BUD - until I insisted that there is another earlier connection flying via VIE. In the end and after some discussion we were rebooked on the KL flight to VIE and onward on the OS flight to BUD. (I had requested OS AMS-VIE-BUD). In the end we made the quite simple direct turnaround.

Never ever give up insisting that you need to be rebooked on the next AVAILABLE flight - no matter which airline it is. They have to rebook you. It pays out to know your rights.

Anyway getting an extra day in Paris is cool too - however AF will provide you with a hotel voucher for an airport hotel.