Paris might be known for the Eiffel Tower and the Arc de Triomphe, but the sight capturing an unlikely amount of attention at the Olympics is the French police.

The city is crawling with law enforcement. They swarm metro stations, street corners, landmarks. They guard checkpoints around venues and the river. There are 35,000 deployed each day, rising to 45,000 for the opening ceremony on Friday.

Forty countries, including Morocco and Brazil, sent officers to help. But it’s the French national police and military gendarmes, with their distinctive side caps and sleek uniforms, that have become as much a symbol of these Olympics as croissants and a rancid river.

Tourists have speculated that the fitness standards, particularly of the gendarmerie, must be higher than those of the NSW or Victorian forces. “I can’t stop staring,” said one female visitor, speaking on the condition of anonymity to avoid upsetting her husband.

Positive attention is a pleasant change for French police and gendarmes (soldiers with power over civilians), given their chequered relations with civilians.

They’re famous for a tendency to be heavy-handed, particularly after an international incident at a Champions League final in Paris two years ago when they tear-gassed Liverpool fans stuck outside the stadium due to a ticketing snafu.

Only a few months ago a group of police officers were caught harassing protesters in a recording, reported by newspaper Le Monde, that featured sexual remarks, threats and boasts. One officer reportedly said to a protester: “You know you really have a slappable face?”

With the world’s eyes upon them, the French are anxious to avoid further scandals. President Emmanuel Macron last year put the country on notice that the “image of France” is at stake.