The Catholic Church will not marry anyone on account of them having a child together. Marriage is a free-will choice between 1 man and 1 woman not in an insestuous relationship.
The better question I think is, is a marriage or romantic relationship between first cousins considered insestuous? I'm not sure but I think technically it isn't even though it's not typically an accepted cultural norm. There is a lot to consider there.
The best course of action is to speak with an trusted, orthodox priest and pray, pray, pray.