I ask because I recently seen this coat of arms at my school:
Which is the coat of arms of the city of Cadiz in Spain. Which from a cursory glance at wikipedia it seems its based on a story of Hercules. And then I remembered a flaired user claiming that many native myths were quickly incorporated into Christianity. So would later Christians have believed in a Hercules or a Trojan War?
The association between Cadiz and Heracles probably has more to do with the fact that the the city sits on the Strait of Gibraltar, whose Classical name is the Pillars of Heracles. They were supposedly the farthest west that he travelled.
Nevertheless, we could say that Christians have always incorporated the Pagan into their spiritual and physical world. Hercules and Troy in particular were often incorporated into civic mythology. For instance in Venice, which is what I know the most about, the Venetians decided that aside from their own Christian pedigree, they were by translation the city of St Mark, the first city on the Venetian Lagoon had been founded by Antenor, a Trojan prince who fled the sack of the city Aeneas style. If I remember correctly the first instance of the Antenor foundation myth comes from a chronicle written in the tenth century, but assuming that it was at least a semi popular belief we might back date it a few hundred years. This classical root seeking only became more pronounced during the renaissance when people like Andrea Dandolo, the great codifier, editor and fabricator of Venetian history really began to dig deep into Classical texts.
As for Heracles, in the Middle Ages (and before, there was a golden Heracles inscribed on one of the gates of Constantinople for protection) he and other classical heroes was seen almost as guardian angels, invoked along with the saints for protection. For instance he appears on the outside of Saint Mark's basilica on two late antique reliefs looted from Constantinople in 1204. If I recall correctly he also pops up in the same capacity on Siena Cathedral and was on the previous Cathedral of Milan.
While I can't make a general statement other periods and have really only made a tiny scratch on the surface, I think it is possible to say unequivocally that Christians, from the beginning, incorporated huge amounts of pre Christian myth and meaning into their day to day lives. Christianity does not really represent a break with the pagan past but rather a development. By and large the memories of the pre Christian era survived and while I was discussing Classical myth many modern fairy stories, superstitions and customs have their roots in beliefs held long before the first church was ever built.