Connes was a member, according to the link. But, as was also mentioned there, there is a rule that members retire at age 50, so by that rule he is no longer a member.

Connes was a member, according to M. Mashaal "Bourbaki: A secret society of mathematicians", AMS 2006 (translated from the French by A. Pierrehumbert). It says so on page 18; see the link. But, as was also mentioned there, there is a rule that members retire at age 50, so by that rule he is no longer a member.