The French are hotly tipped as the favourite. And they sit at the top of the list of a recently published index of the teams' multiculturalism. A majority of the French team has roots outside France's continental borders, from places as far-flung as the Indian Ocean island of Reunion to the Caribbean territory of Guadeloupe and many countries in between.
Football in France, as Duke University's Laurent Dubois notes, has become "a terrain of incredible political investment and symbolic meaning," beginning perhaps most noticeably with the country's triumph in the 1998 World Cup. That famous side was led by Zinedine Zidane, the son of Algerian immigrants, and a vanguard of other players with origins in France's former colonies.
The national team was hailed as the emblem of French multiculturalism. Thierry Henry, the legendary French forward whose parents emigrated from the Caribbean and who grew up in the rough-and-tumble environs of Paris, recalled an elderly women embracing him and thanking him for giving the country its greatest moment since liberation from the Nazis.
"That's when I realised how powerful sport is," he said later. "Even if I don't completely understand it."
But the rosy picture didn't stick. When France stumbled and collapsed in subsequent tournaments, the spectre of racial divisions and discord was raised. Nationalist politicians groused against a purported lack of patriotism in the squad, a theme echoed in countries such as the Netherlands and Belgium, as well.
The current tournament, despite the optimism surrounding France, also has been shadowed by racial controversy. Because of a tawdry investigation involving a sex tape and an alleged case of blackmail, the country's best striker, Karim Benzema, was excluded from the squad by coach Didier Deschamps.
Angry about his omission, Benzema, who is of Algerian heritage, claimed that Deschamps had "bowed to the pressure of a racist part of France", referring to the French far-right, led by the ascendant National Front.
Marion Le Pen, the granddaughter of the party's founder, tweeted that if the striker wasn't happy, he should go play for "his country"- a reference to Algeria, not France.
"This is not a good debate for France," Prime Minister Manuel Valls cautioned.
There are similar unseemly conversations elsewhere. Last month, a far-right German political movement complained when a beloved chocolate brand featured the non-Teutonic faces of a Turkish and an African boy on the candy's wrappers.
"They don't stop at anything," the anti-Islam, anti-immigration group Pegida said on its Facebook page. "Can you really buy them like that, or is that a joke?"
What the bigots didn't realise was that the photos in question were childhood snaps of two beloved German football players - Jerome Boateng, whose father came from Ghana, and Ilkay Gundogan, a midfielder of Turkish origin.
Of course, the diversity of a national team isn't a reflection of the harmony of a nation. The Euro 2016 tournament will take place in the shadow of terrorism. Indeed, the gruesome Isis (Islamic State) attacks in Paris in November were aimed in part at disrupting a friendly match between France and Germany, and security concerns linger.
The bombings this year in Brussels had a profound effect on Vincent Kompany, the thoughtful captain of Belgium's national team. Kompany grew up in the largely poor, predominantly immigrant neighbourhoods of the capital that have now come under scrutiny for their perceived ghettoisation.
"The reason why it hurt me so much is because they're not people of a religious faction, they're people that have been able to fall off the grid, and people have been able to indoctrinate them," Kompany said on CNN.
When he speaks, people listen.
Dubois wrote: "The team is beloved not just for its successes on the field but also because its diversity represents Belgium as it is today."
But that doesn't resolve the country's challenges. "I think it was inevitable," Kompany said about the Brussels attacks, "because I only used to see politicians in our neighbourhoods once every six years when they needed to come for votes."