Vueling will not transfer luggage to Air France, and neither will Air France transfer luggage to Vueling.

This is because you are travelling on separate tickets. Whether and if there is an interline agreement would only be a question of interest if you were travelling on a single ticket; but you already fall at the first hurdle.

It is not possible to buy a ticket involving travel on both Vueling and Air France that would offer the benefits of interlining.

(To the best of my knowledge, the only non-oneworld airline that VY has an interline agreement with is Hainan Airlines, and I don't know if that agreement is even still in operation)

I would recommend you come up with a more robust solution to your travel needs; if you must use separate tickets in this manner, make sure to allow sufficient time between the tickets to assist you in recovering from the many calamities that may arise - weather, delay, flight disruptions, late delivery of luggage, or even loss of lugage, from your first flight. You will need to wait for the luggage delivered from the first flight, and bring it to the drop-off desk of the next flight - which may be in a different terminal - before the check-in deadline of the second flight. If, for whatever reason and through no fault of your own*, you miss the check-in deadline of the second ticket, you will lose the value of the second ticket.

*Not your fault: however, by booking separate tickets, you are entering into 2 separate contracts with 2 separate airlines, guaranteeing to be present by the check-in deadline for both. By booking 2 separate tickets close together, you are undermining your chances of actually being able to meet the terms of the second contract. Therefore, it is in your own best interests to either book all travel on one ticket (whereby any such delays become the problem of the next airline - they will have to rebook you), or to allow as much time betwen tickets as possible (meaning that, even if there is a problem or delay, you still have some "slack" in order to not miss your connection).

FYI: when I travel on separate tickets, I always make sure I have either an overnight stop at the connection, or some other mechanism to fall back on so that the second ticket is not jeopardized (like booking the first ticket early enough that, even if scrapped, there is at least one more flight later that day that I could take in its place)