Is it possible to be of irish descent and have a very french last name?

My last name is probably the most french name you will ever hear in your life. I am not going to say it here, but I know it is french. The only problem with my french name is that, my dad, grand-father and great grand-father always said we were of irish descent. My dad told me a tale about, how my great... show more My last name is probably the most french name you will ever hear in your life. I am not going to say it here, but I know it is french.
The only problem with my french name is that, my dad, grand-father and great grand-father always said we were of irish descent.
My dad told me a tale about, how my great grand-father had to be chained to a tree once, because he was very mad and were in such a rage.. that no one could calm him down, and that he was like that because he was irish. And it's something both my great grand-father, and my grand-father said. That they were of irish descent.

We do not have paper or genealogy that can go that far and verify this, and the internet searches I did never really gave an answer to this.

What do you think?
Update: How could I verify this.
Internet didn't quite answer, and there is no paper in my family to confirm this.

Go to irish myself and ask? (No, i'm kidding)

What should I do?
Update 2: ...
go to irish..
ok I need sleep,
I meant Ireland..
Sorry
Update 3: Ted: I know genealogy is more then just a tale my dad told me.

But I do not wish to post personal informations about me on the internet. I can send them to you by mail if it's possible.
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