Europe's four-yearly football extravaganza is taking place just seven months after jihadists killed 130 people in the French capital and there are fears the tournament could be a target for more terror attacks.
Germany defender Jerome Boateng became the first high-profile player to say he was banning his family from coming to the stadiums for the tournament because he was concerned for their safety.
"My family and children will not be coming to the stadium. The risk is simply too big," he told Sport Bild weekly.
The immediate concern though was the industrial unrest and political turmoil over controversial labour reforms that look set to continue into the championships despite the government's pleas for unions to halt their action.
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In the latest of four months of strikes, union supporters blockaded incineration centres in central Paris, causing uncollected rubbish to pile up in 10 of the capital's 20 districts.
Paris Mayor Anne Hidalgo called for an end to the strike action and promised to get the rubbish collected as soon as possible.
Uncollected black refuse sacks were also accumulating in Saint-Etienne, the central city which will host four Euro 2016 matches.
Rail workers locked in one of the most obstinate strikes said they would continue to disrupt services tomorrow, extending their action to a ninth day in Paris and several other regions.
Unions were still chewing over an offer from the SNCF rail operator to end their dispute.
Hundreds of union activists lit flares in a protest rally in the Gare du Nord station, the departure point for Eurostar trains to Britain and other services to northern Europe.