To be honest it could be a mix of polearms, pikes, and missile weapons.
It's worth noting that in the 1480s the French were making use of longbows, both in the ordonnance companies and the francs-archers, so French archers shouldn't be ruled out.
There was also a project in the early 1480s to train a professional French infantry force in Swiss pike tactics. It's not clear if they were predominately pikemen or more of a mixed arms force. It's also not entirely clear what happened to them - after the death of Louis XI in 1483 the camp they were training at was broken up, but I haven't found a concrete answer as to what happened to this infantry force. Was it a short-lived experiment which never saw action, or were these newly trained troops sent to garrison the Flemish border?
However it's worth thinking about who the French mercenaries at Bosworth actually were - I highly doubt they would be an organised body of troops from the French military systems, such as the ordonnance companies, the francs-archers, or the new infantry described above. Surely they would be more of a loosely organised, informal group? Though of course if experienced soldiers they would very possibly have experience serving in the aforementioned organisations, and there is potential for the mercenaries to include soldiers trained in longbow archery and pike tactics.... But perhaps i'm wrong!!! I'd love to find out more.