Thanks for the question. For the others reading this posting, let's first define some terms:
first cousins are the children of their parent's brothers and sisters.
a second cousin is the child of your parent's first cousin.
First cousins share a grandparent, second cousins share a great-grandparent, and third cousins share a great-great-grandparent.
We have already answered a similar question on second cousins. You are welcome to view it here:
Church law used to prohibit marriage between second cousins. It was not a strict ban because the local bishop could and often did grant dispensations from the rule. Under current law (in effect since 1983), there is no obstacle to a marriage of second cousins.
To be sure about your question on first cousins, you should consult your pastor, since we are lay volunteers, not trained experts in Church law.
If you wish to save time, trying searching for answers to your questions using our search engine:
I hope this helps,
Mike and Andrew