The Barcelona forward set up the opener for Corentin Tolisso after eight minutes and followed up with the second just after the half-hour in Albania's first match at the new Arena Kombetare.
It was the perfect way for the world champions to celebrate Didier Deschamps' 100th match as manager of France, who were already qualified, and ensured they finished two points ahead of Turkey in Group H.
Chelsea striker Olivier Giroud, named in the side with Kylian Mbappe out through illness, hit the woodwork in the second half of a dominant display.
France got off to a superb start as Tolisso met Griezmann's cross from the left with a superb header at the near post.
Griezmann was at the heart of most of France's good play and he doubled the lead in the 31st minute.
A deep cross from Presnel Kimpembe had Albania back-pedalling and Leo Dubois cut across the area. He did get a lucky deflection off Frederic Veseli – who was once on the books of Manchester City and United – but his pull-back was clinically tucked away by Griezmann.
Griezmann almost created a third before the break from a corner but Clement Lenglet headed over unmarked from seven yards.
Albania threatened early in the second half as Elseid Hysaj slid in to shoot wide and Rei Manaj had an effort blocked by Lenglet.
But France retained control and Giroud held off a defender to force a save from goalkeeper Etrit Berisha.
Giroud tested Berisha again with a fierce shot from a tight angle and was then unlucky when he rattled the woodwork after 72 minutes.
Albania had another couple of opportunities through Hysaj and Keidi Bare in the latter stages but France were not to be denied.