The eight-minute video (see below), which has been watched more than 600,000 times on Youtube, shows the later stages of an arrest taking place on rue Pierre Coubertin in the town of Joué-les-Tours, in the Indre-et-Loire department.
According to local daily La Nouvelle Republique, the two officers had stopped a car driving erratically on the street early on Sunday morning, and found the driver highly intoxicated.
The latter became uncooperative and unruly when asked to submit to the alcohol test, and a female passenger intervened, allegedly biting one of the two officers, according to a representative of the Unité SGP police officers union, who spoke to France Bleu radio on Tuesday.
The video begins with one officer attempting to subdue the driver and keep him on the ground, while the second officer grapples with one of the female passengers, striking her freely with his baton, including once, with force, on the face.
A few moments later, the same officer goes to his vehicle to retrieve tear gas, according to French daily Le Parisien, which he sprays in the face of the woman, before also spraying a second woman directly in the face.
French Interior Minister Manuel Valls on Tuesday confirmed that the Inspectorate-General of the National Police had been informed of the events shown in the video.
Prosecutors in nearby Tours have said they intend to summon the two officers to tell their version of events, with a view to opening a full investigation, according to Le Parisien.
For his part, Valls warned: "There is no place in the police for violence, or views that have no accordance with the ideals of a republican police force."
"The police should be beyond reproach, and the vast majority of police officers do a difficult and remarkable job," Valls was quoted as saying by French daily Libération.
There has been overwhelmingly angry reaction from observers in France, with most condemning the actions of the police officers shown in the video.
Journalist Jean-Yves Viollier took to Twitter to express his outrage. "The policemen from Joué-les-Tours, gassing and beating a woman, should be suspended. They are a disgrace to French police."
Les policiers de Joué-les-Tours, matraquant et gazant une femme, doivent être suspendus. Ils sont la honte de la police française.— VIOLLIER Jean-Yves (@JYViollier) August 20, 2013
A police union representative warned against drawing conclusions from the video without knowing all the facts.
"The video may seem shocking but we don't know the context," Gaelle James of France's second-largest police union, Synergie Officiers, told AFP.
She said the officer involved had reacted after being pinned down by the woman and bitten three times.
"He clubbed her to get away," James said. "He had to intervene under very difficult conditions. We cannot forget that violence against the police is increasing. This doesn't shock me."
The following is the eight-minute video in question, entitled "Honte à la police francaise" (Shame on French police), by uploader Nasser Tkt.
It contains moments of violence that some readers might find upsetting.