Soldiers from an anti-terrorism military unit patrolled the Champs-Elysees avenue on Saturday while police vans circled the Arc de Triomphe, looking to protect some of the capital's most famous sites from any repeat of the unrest that shook France last week.
Nunez has mobilised 70,000 police nationwide for Saturday's demonstrations, 10,000 more than on October 17, when a wave of vandalism and looting shocked the country and raised questions about the government's ability to maintain order.
Anger over living costs and strained public services has drawn students, workers and unions onto the streets in recent weeks, but authorities say radical militants and bands of young looters have exploited the protests to sow chaos.
Speaking to police in Paris, Nunez warned officers that they would face attempts to target shops, public institutions and security forces.
"We have to be ultra, ultra responsive. We have significant calls for disruption from political groups and quite simply from criminals," he said.
"It is going to be a long day."
Many shopkeepers in Paris boarded up storefronts, while luxury retailers beefed up security.
Business groups have urged stores to remain closed after thousands of shops and businesses were damaged or looted across France last weekend.
Several of Paris's best-known cultural institutions, including the Louvre, the Musee d'Orsay and the Grand Palais, will close for the day to avoid being caught up in any turmoil.
More than 20 metro stations were also shut.
The location of Saturday's main Paris demonstration remained unclear after police sought to move organisers away from the city centre towards the southeastern fringes of the capital.
"The declared route poses serious risks of disturbances to public order, notably because of the high concentration of businesses similar to those targeted during the weekend of October 17-18," the Paris police prefecture said.
The last-minute decision angered some on the left.
"Once again, those in power are creating disruption for the marches and impossible deadlines for organisations to reorganise themselves. These methods are multiplying across the entire country," hard-left leader Jean-Luc Melenchon wrote on X.
Authorities have sharply restricted demonstrations across much of France.
Marseille reversed an earlier ban and authorised a union march, while protests remain restricted in central Lyon.
Union rallies will also go ahead in Strasbourg, but bans remain in force in several other cities including Nancy, Metz, Besancon, Belfort, Rouen, Le Havre, Toulon and Limoges.
The first authorised march began mid-morning in Orleans, about 120km south of Paris, to protest against Marine Le Pen's far-right National Rally, which is holding a congress in the city this weekend.
Tensions were heightened by a shooting west of Paris on Friday in which a gunman suspected of acting out of Islamophobic hatred killed one person and wounded four others, including a 12-year-old girl.
