The match kicked off late at the Stade de France on Saturday because the hosts mistakenly played the Andorran anthem before the stadium announcer then apologised to the "Armenian fans" after the correct song was played.
"President Macron presented his sincere apologies for the scandalous gaffe by the French football federation with our national anthem," he tweeted.
"The French President considered the gaffe as an 'unacceptable error' and he appreciated the reaction of our players," he added.
President Macron's office confirmed the apology to AFP.
French coach Didier Deschamps has also said sorry to his Albanian counterpart, Edoardo Reja, for the error.
France, top of Group H on goal difference, host Andorra on Tuesday in the next fixture of their Euro 2020 qualifying campaign and Albania face Iceland.