Since this name ends in -ic, I strongly doubt that Ludovic is the medieval Latin form of Ludwig. -ic is not a latinate ending; at most -is is (like in Clovis).It seems to me that Ludovic is actually the (medieval) French form of Ludovicus, and that name actually is the proper Latin form of Ludwig. [noted -ed]Also compare the French name Frédéric: it comes from Fredericus, which is one of the Latin forms of the ancient Germanic name Friduric (other Latin forms include Fridericus and Friduricus). So, just like the -ic in Frédéric is a gallicization of Latin -icus, so is the -ic in Ludovic.
It seems to me that Ludovic is actually the (medieval) French form of Ludovicus, and that name actually is the proper Latin form of Ludwig. [noted -ed]
Also compare the French name Frédéric: it comes from Fredericus, which is one of the Latin forms of the ancient Germanic name Friduric (other Latin forms include Fridericus and Friduricus). So, just like the -ic in Frédéric is a gallicization of Latin -icus, so is the -ic in Ludovic.