The French attack stammered until Benzema came on in the second half and Mbappe got him ready for the first game.
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Mbappe then scored France’s second goal as world champion, who had already qualified for Qatar 2022 after Kazakhstan’s 8-0 demolition on Saturday, finished Group D with 18 points in eight games.
Finland, who were hoping for a playoff berth, finished third with 11 points, one behind Ukraine who beat Bosnia 2-0 away to take second place.
“We wanted to finish in style and we are happy that we did. Now we are looking forward to the World Cup. With the team we have, it is natural to think about [winning] that, ”Benzema said.
France have now scored in their last 18 games, tying a record dating back to 1999-2000.
Finland were the last team to draw a draw against Blues and it looked like they could repeat the feat, but Benzema’s entry in the 57th minute marked the end of their hopes.
Didier Deschamps had made five changes to the team that hammered Kazakhstan, with Benzema and Kingsley Coman on the bench.
The duo’s absence was clearly felt as Blues struggled to create chances against a compact Finland side.
Shortly before half-time, Léo Dubois injured his thigh and was replaced by Benjamin Pavard.
Finland started the second half coolly but the French defense remained vigilant and the visitors stepped up a gear when Benzema replaced Moussa Diaby.
They were rewarded in the 66th minute with Benzema finding the back of the net with a low deflected shot after a nice one-two with Mbappe, who found the Real Madrid striker with a back heel.
Ten minutes later, Mbappe edged out three Finnish players on the left flank before finishing with a superb curling shot into the far corner of the net for his 24th international goal.
It was Mbappe’s fifth goal in two games after scoring four against Kazakhstan.
“The stakes were higher for Finland than for us tonight, but we did what we had to do,” said Deschamps. “It was a very positive year for France, with the exception of those fatal 10 minutes during the round of 16 of the European Championship against Switzerland. ”