Barcelona star Griezmann curled in the opener in the 19th minute before Andriy Shevchenko’s Ukraine drew level courtesy of an own-goal by the unfortunate Presnel Kimpembe just before the hour mark at an empty Stade de France.
It is a result that immediately puts the defending world champions on the back foot, with only the group winners automatically qualifying for next year’s finals.
France make the long trip to Central Asia to play Kazakhstan on Sunday before stopping off in Sarajevo for another game against Bosnia and Herzegovina next Wednesday.
Les Bleus will also face Finland in the five-team Group D, and a brace by Teemu Pukki saw the Finns draw 2-2 with Bosnia in Helsinki in Wednesday’s other game.
“We could and should have put the game to bed in the first half. We ran out of steam a bit in the second half and we were up against a good team too, although the goal we conceded was avoidable,” coach Didier Deschamps told broadcaster TF1.
“We are obviously disappointed. It is the first step, we have two more games to come which won’t be easy either.
“Qualifying is a long road and it won’t be plain sailing.”
Eight of the players who started the 2018 World Cup final win over Croatia in Moscow were named in Deschamps’ starting XI here, with Paris Saint-Germain centre-back Kimpembe, Juventus midfielder Adrien Rabiot and Bayern Munich winger Kingsley Coman the only exceptions.
Another of the 2018 final heroes, midfielder Paul Pogba, came on as a second-half substitute after Ukraine had cancelled out the lead given to the hosts by Griezmann.
He arced a shot from the right-hand edge of the penalty box into the far corner to score his 34th international goal on the occasion of his 87th cap.
It was a goal that surely would not have stood had VAR been in use for this game, as Raphael Varane’s ball forward at the start of the move was aimed at a Benjamin Pavard in an offside position.
However Ukraine, with a team featuring six starters from Dynamo Kiev, overcame any sense of injustice from that to equalise with more than a slice of luck.
As France struggled to clear their lines, Oleksandr Karavaev intercepted the ball wide on the right before cutting it back for Serhiy Sydorchuk.
His first-time shot was going wide of the right-hand post before it struck Kimpembe and trickled into the opposite corner, beyond the reach of goalkeeper Hugo Lloris.
Ukraine, who are ranked 24th in the world and will be at Euro 2020 in June, will hope to build on this result when they host Finland in Kiev on Sunday.