A first thing to note is that there is a slight translation issue: in current (post-WW2) French, the term militant has lost its original aggressive "military" edge and simply designates an active supporter of a movement or ideology, political or religious. It is usually translated in English as "activist". A French militant is expected to be active: going to meetings, marching in demonstrations and protests, putting up posters, distributing flyers, recruiting other people to the cause etc. Of course, some militants, notably those from radical organizations, can indulge in violent activities, from street fights to terrorism, but your regular militant may be just be a registered member of a party or a trade union who pays their fees and goes to meetings.
During the war, a Gaulliste was a member of the Resistance, but the term morphed after 1945 to just mean "active supporter of de Gaulle", a person doing regular militant stuff, ie activities favourable to de Gaulle's policies. Because de Gaulle only created one political party, the Rassemblement du Peuple Français (RPF, 1947-1955), the term Gaulliste was never quite precise and was claimed over the years by anyone who declared themselves adherent to Gaullisme, which could mean a lot of things depending on what they liked in de Gaulle's actions and ideas: there were "left-wing Gaullists" and "right-wing Gaullists". Jacques Chirac's Rassemblement pour la République (RPR, 1976-2002) was the last party to claim a direct Gaullist legacy, so there were technically Gaullist militants until the 21th century (though they were more likely to be called chiraquiens).
However, there was a Gaullist organization that could be called a militia: the Service d'Action Civique (SAC), which started as the security arm of the RPF at a time when violent street brawls were common between right-wing and left-wing supporters, notably those of the French Communist Party. The SAC also had roots in the wartime Gaullist intelligence services, and it held a tradition of secrecy and distrust of official authorities. Note that the SAC archives were destroyed, making the history of the organization entirely dependent on other sources, notably newspapers articles, court proceedings, and oral testimonies (by often unreliable narrators). It thus still imprecise. Notably, it is difficult to establish with certainty if a person was a SAC member, which has allowed people to claim or deny being one, or to accuse someone of being one.
Founded officially in 1960 by Jacques Foccart, the éminence grise of de Gaulle and eternal "Mr Africa" of the French Republic, the SAC was initially an activist organization composed of hardcore faithful Gaullists doing security during meetings and demonstrations. Street brawls between colleurs d'affiches - the activists who put up posters during election periods - are an old French tradition, and the SAC provided the muscle for this, tough men who did not mind using their fists to punch opponents, with the occasional knifing and shooting. The SAC also acted as a private security "company", providing protection for Gaullist leaders and their friends. Through Foccard, the SAC had a direct link with de Gaulle, and access to secret funds (Audigier, 2018). However, the SAC was not involved in the fight against the pro-French Algeria OAS terrorist organization, due to the divided loyalties of many SAC members, including its leader Pierre Debizet in the 1950-1960s, who was against Algerian independence.
For Audigier, the SAC remained an ideologically Gaullist force until 1969 (though tainted due to collusions with organized crime, see below) but lost steam in the 1970s after the death of de Gaulle and the rise of Chirac, whose own RPR had hundreds of thousands of registered activists and its own security branch. The SAC became a mostly anticommunist, far-right organization using violence and intimidation against political opponents. For instance, in 1980, a show of singer Serge Gainsbourg, whose reggae version of French anthem La Marseillaise was found blasphemous by right wingers, had to be canceled in Strasbourg following a bomb threat and the presence of far-right activists, including paratroopers and a local SAC delegation (famously, Gainsbourg got on stage anyway and sang the original song with his haters joining him).
According to a parliamentary report (Odru, 1982), the SAC was never a mass organization. It may have had less than 10,000 members before 1968, doubled or tripled that number after May 1968, and was later purged from its most dubious members, going back to low numbers, possibly 8000-10,000 in the late 1970s, with half of them actually active. It was down to less than 5000 in 1981. Audigier believes that actual numbers were much smaller, about 3000 in 1968 (Audigier, 2018). In 1982, membership was primarily male, with a notable recruitment in law enforcement (10-15% police officers). For a while, it benefited from a relative protection by police authorities and there was a certain porosity between the SAC and law enforcement. In 1982, 50% to 75% of SAC militants were also registered members of Chirac's RPR: while the SAC was a distinct organization from the mainstream RPR, it was still close to it (Odru, 1982).
What made the SAC particularly infamous was its reputation of being a parallel police organization used by Gaullist operators/politicians like Jacques Foccard and Charles Pasqua for illegal intelligence gathering (such as collecting data on left-wing activists), infiltration (of universities and trade unions), and violent operations. The SAC hired - or at least was in direct contact with - organized crime, who lent it "muscle" when required. In some cases, these relations went back to WW2, when the Resistance relied on the criminal underground for clandestine activities. As a result, the SAC was named in numerous criminal cases, from pimping and robberies to large-scale drug trafficking - two SAC members were involved in the "French Connection" - where the accused were SAC members or affiliated in some way to the SAC. Even if such crimes were not directed by the government and were not SAC operations, it remains that this movement had close links with the organized crime and kept known criminals in its roster.
This eventually caused the demise of the SAC. On 18 and 19 July 1981, the head of the SAC in Marseilles, police officer Jacques Massié, was murdered with five members of his family, including his 7-year old son, by other SAC members who accused him of embezzling the organization's money to fund his lifestyle and feared that he would give confidential SAC information to left-wing organizations. The gruesome tuerie d'Auriol - The Auriol killings - led to a public outcry that resulted in the banning of the organization, now considered to be a criminal one, by President Mitterrand in August 1982.
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