Translation:You were not at all familiar with this cousin.
In negative constructions, adverbs which would normally follow the verb are placed after pas. http://french.about.com/library/weekly/aa060300.htm
Long adverbs which specifically modify the verb are placed directly after the conjugated verb: http://french.about.com/library/weekly/aa060300.htm
French adverbs in negative construction are placed after the "pas" instead of after the conjugated verb. http://french.about.com/library/weekly/aa060300.htm
There is no distinction in the English "cousin". It is the child (either male or female) of a parent's sibling, i.e., your aunt/uncle. So "cousin(e)" would be translated only as "cousin". "Niece" is the daughter of one of your own siblings. "Nephew" is the son of one of your own siblings.
"Recognize" would be reconnaître, whereas connaître is "to know", "to be acquainted with", "to be familiar with", "to know about", etc.