Sounds like Asterix at the Olympic Games (2008).
Asterix at the Olympic Games (French: Astérix aux Jeux olympiques) is a 2008 French fantasy comedy film co–directed by Frédéric Forestier and Thomas Langmann, and written by Langmann, Alexandre Charlot and Frank Magnier, based on characters from René Goscinny and Albert Uderzo's Astérix comic series. It was filmed primarily in Spain throughout 2006.
Astérix and Obélix must win the Olympic Games in order to help their friend Lovesix marry Princess Irina. Brutus uses every trick in the book to have his own team win the game and get rid of his father Julius Caesar in the process.
The film is loosely adapted from the original Asterix at the Olympic Games comic book. The love story subplot between Lovesick and Irina was not featured in the original story. Brutus, portrayed here as a comical villain with no relation to his depictions in Asterix comics, is the main antagonist, although he was not even featured as a character in the original comic book.
The Wikipedia page for the original comicbook version of this story (from 1972) mentions the Romans having blue tongues, as a result of having drunk a special batch of Getafix's magic potion, in order to cheat in the games.
At the games, Asterix and the Roman athletes are beaten at every turn by the Greeks, causing a dilemma to the Olympic officials. Although their victories prove what they've believed all along (that Romans are decadent barbarians and the Greeks are perfect beings), too much success will reflect badly on the country's reputation, so they announce a special race for just Romans. After the announcement, Asterix and Getafix start talking, very loudly, about a cauldron of magic potion left in an unguarded shed. Eager to win, the other Roman athletes steal the potion that night.
The race begins, and the Roman athletes easily beat Asterix - they all overtake him and cross the finish line simultaneously. After the race, Getafix accuses them of having used magic potion and, when the Romans deny the accusation, Asterix sticks his tongue out at them. When the Romans return the gesture, it is revealed that Getafix had added an extra ingredient to this particular batch of potion and the Romans now have blue tongues from drinking it. They are disqualified, and Asterix is declared the winner.