Hi Becky,
If both you and your cousin have also taken the basic Family Finder autosomal (aka auDNA or atDNA) at FTDNA then you should be able to find information about your DNA match with him in your Family Finder matches at FTDNA. From your profile it appears that you have also tested at Ancestry, so if your cousin has also tested there then you would be able to see information about your match DNA match with him under the DNA matches at Ancestry. Ancestry only does autosomal DNA tests.