US President Donald Trump has said the NFL "could have probably postponed" Sunday's game in Paris between the Pittsburgh Steelers and New Orleans Saints due to street protests in the city.

France is bracing for more demonstrations Saturday against the high cost of living, with museums closing and the government deploying a larger security presence to prevent a repeat of last week's violent unrest.

The game on Sunday - the first ever NFL regular-season game held in France - is taking place at Stade de France in Saint-Denis, just north of the capital.

"I think maybe it's looking like tomorrow is going to be a bad day in France, so you worry about it," Trump told reporters.

"I would have said the NFL could have probably postponed that match, because France is really in trouble."

The US State Department issued a security alert late on Thursday, saying: "Numerous groups submitted plans for protests on Saturday October 24. Americans in Paris for the NFL game on Sunday October 25, should also exercise caution and be aware of their surroundings.

"While permits may be filed for demonstration routes, last-minute changes can happen and protests can occur outside planned routes."

NFL Commissioner Roger Goodell said this week that preparations were made in consultation with US and French authorities.

Street protests, he said, "are not unusual in France". The league did not immediately respond to a request for comment on Trump's remarks.

Soccer team Paris Saint-Germain's game against Lyon has been moved from Sunday to Monday evening at the request of Paris police.

The game was scheduled for Sunday night in Parc des Princes.

Steelers quarterback Aaron Rodgers said on Friday that "the NFL is alert to what's going on".

He added: "This game means a lot to the NFL. If it was unsafe, then I'm sure we wouldn't be here."

A weekend event for Steelers fans was cancelled on Thursday because of security concerns.