After they become acquainted with Remus and Sirius, do Fred and George figure out that they are Moony and Padfoot, respectively? After that, I would assume they would connect James and Peter.
It seems like they would, but I don't think they ever find out.
Plus, according to the Harry Potter Wikia article on Fred Weasley:
Fred and his brother George regarded the Marauders with a kind of idolatry... The twins did not, however, work out that two of the Marauders were two of their friends in the Order of the Phoenix: Remus Lupin and Sirius Black. Neither did they discover that Prongs was in fact Harry's father, James, and that Wormtail was actually Death Eater Peter Pettigrew."
And the HP Wiki is usually correct with Canon.
I don't believe they did at the time they had the map, since A) there would have been no way (or reason) of knowing enough details of those people's pasts, and B) I don't feel like they would have been too interested in finding out who it was, more just in using the Map. However, later on after Harry and the others know, and especially after the OotP is reestablished, they may have found out.