The £5m campaign, created by Abbott Mead Vickers BBDO, is attempting to align the chocolate bar with support for the team and will see the product’s packaging show the word "Believe" instead of the Mars logo.
Starting on Sunday with a 60-second TV ad, the campaign will also run across cinema, radio and digital in the run-up to the tournament, which begins on 10 June.
Led by England strikers Danny Welbeck, Harry Kane and Jamie Vardy, the spot shows a madcap throng of football fans, dinner ladies, and animals crossing the channel in dingies and floats.
When they land on a French beach, a man dressed as a medieval knight asks for directions to the Stade de France, the country’s premier football stadium which will host the opening ceremony on 10 June and final on 10 July.
Mars will also call on the public to submit "singing selfies" – filming themselves as they sing the lyrics to an England song and sharing this online using the campaign hashtag, #Believe. "Singing selfies" will be launched on the day of England’s first match on 11 June.
The spot was written by Michael Hughes and art directed by Dalatando Almeida. Sam Brown directed the ad through Rogue Films, while MediaCom handled the media planning and buying.
Mars has been an official sponsor of The Football Association, the organisation which administers English football and the national football team, since 2009.
Greg Kent, the brand manager for Mars, said: "International football tournaments ignite the passion of England fans like no other sporting event. Up to 20 million people are set to watch each match at Euro 2016 with a potential audience of 15.3 million UK football fans predicted to be on Twitter at any one time during a game.
"As we all know, the 12th man can make all the difference in football, and through our multi-channelled campaign we hope we can give the England football team the extra edge they need to go all the way in France."