AF and SQ can interline bags so it is technically possible. That said, being on separate tickets you run a risk that the AF agents won't check the bags all the way through for you. That's a pretty tight connection with separate tickets.

Bring a copy of your SIN-SYD itinerary, preferably one which has the PNR and ticket number on it, and get to the counter at CDG a bit early. Oh, and be very nice when you ask.