By booking an AF-code flight in cooperation with Finnair you get Flying Blue points, but not from an AY-flight. In other words, you don't get FB points from Finnair flights, unless it's a cooperation with a FB partner and you are flying with a FB-code ticket.

The ticket prices also vary according the ticket issuer and luckily for the last six months AirFrance has always offered cheaper tickets in economy than Finnair