Hebert surname assistance

I've asked this question on the French-Canadian list but it's really much broader than that one list. Do you know anything about the French surname HEBERT and its possible connection to Scotland. DNA tests I've taken show some significant French heritage connections: most of the closest surname y-DNA results are all men with the HEBERT surname. One of these men has told me of a significant number of MAXWELL surname ancestors. Those MAXWELLS are all Scottish as are the MAXWELLS in my own family tree. There's some possible suggestions. First of all, the Scots and the French were long allied in their opposition to the English and English national interests. Many Scots studied and were educated in France. One of my own MILLER ancestors learned his printing trade somewhere in France. And, furthermore, my own DNA results show a significant French heritage: about 53% British Islands, 34% French, 11% Scandinavian, and about 2% Middle East. These percentages roughly reflect my family tree as developed and do really reflect the realities of Scottish history. But that doesn't help in my original question. Why can I not tie my substantially identified Scottish and French together with this one particular surname? Why can't I find those connections between the HEBERTS and the STEPHENS surnames. My DNA test results suggest that that should be easily done. But it's proven to be elusive. I would love to learn more about the HEBERTS with any information you may have to share.

My direct email if you prefer this route is jstephens6@cox.net