My father's family is French Canadian from rural Quebec. There is a possibility that they were at least part Native American... I have no clue to the tribe. How can I find out for sure?

They sell DNA kits that provide genetic backgrounds. Here is a good link:How to Find Native American Ancestors with DNA Testing | eHow.com (http://www.ehow.com/how_4739296_native-american-ancestors-dna-testing.html)