The month-long competition starts on Friday and will be held in stadiums across France, which has been repeatedly targeted by Islamist militants including in a series of attacks on November 13 that killed 130 people in Paris.
The England, Wales and Northern Ireland teams are all taking part in the tournament. The Foreign Office website, updated on Tuesday, advised fans travelling to support them to be vigilant at all times and follow the advice of French authorities.
"During Euro 2016, stadiums, fan zones, venues broadcasting the tournament and transport hubs and links represent potential targets for terrorist attacks," the advice read.
A spokeswoman for Prime Minister David Cameron told reporters at a regular briefing that the advice was not a result of specific intelligence.
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"It is not in response to a new or specific threat ... It is in the context of making sure that the government and authorities are doing all they can to provide relevant information for fans," she said.
French President Francois Hollande has acknowledged a heightened threat of terrorism during the tournament and said France was taking all possible measures to keep fans safe.
(Reporting by Kylie Maclellan and Kate Holton, writing by Estelle Shirbon; editing by Stephen Addison)
