That's technically possible but you might have to insist if the option is not offered to you or in case of "can't do" (better travelling first with AF as KL seems more reluctant to interline luggage). Make your way to the luggage desk with your 2nd boarding pass ready. The agent will need your ticket reference and your sequence number.

On my side, for those interested, I got my luggage transfered without trouble on a AF -> KL connection at Stuttgart some weeks ago (BLQ - LYS - STR - AMS), on 2 separate tickets aswell. I also managed the same at Linate on a AZ -> AF connection (BRI - LIN - CDG), same 2 separate tickets situation.