Earlier quoted context omitted.
It sounds like [a] to me, not [æ]. The a in the name Jacques is pronounced as in the word father . The a in the name Jack is pronounced as in cat.
As someone who has heard the name "Jack" pronounced by Americans many, many, many times in their life... that Jaques video sounds entirely in-range of the variety of pronunciations I hear for Jack.
Something I find interesting is that Americans say the a in the word taco (a word borrowed from Spanish) with the a as in father, that is, [ɑː], but English people say the a as in cat, [æ]. Different dialects approximate the Spanish [a] differently.