According to family tradition (as in, what my father told me, backed up by a hand-sketched family tree), the Henry part fled France after the 1685 revocation of the 1598 Edict de Nantes (which meant that Protestants were no longer protected by the French King) and settled in Ireland with British royal approval as a side-battle of the English/British religious wars. My ancestry.com research starts when descendants entered America, including English colonies in what is now Canada. They provide access to overseas documents, but I have never thought it worth the added cost.
Some of those old records contradict each other, or just engage in obvious falsehoods. For example - the Corliss family tree book states that the original Corliss came from Belgium in the 1600s, but there was no Belgium as we know it today until the 1830s, when the Flemings and Walloons revolted and separated from Dutch rule and selected a German Prince to be their King. The Corliss aunt who wrote the book included a picture of King Albert I with a caption hinting at "family resemblance". She deserves a "coocoo".