The profile of the baffeur (Damien Tarel) is certainly interesting, notably his belonging to, or strong sympathies with, the far-right anti-Semitic Royalist organisation Action Française, which was created over 120 years ago (during the Affaire Dreyfus) and has (or claims anyhow) some 3,000 members in France.
(incidentally, his trial is this afternoon in the Drôme department, it’s a “comparution immédiate”, a common procedure in French law which follows police custody/a garde à vue whevener the facts are clearly established and don’t warrant a thorough investigation. There were 60,000 comparutions immédiates in France in 2019, out of a total of 780,000 cases treated by the penal system).
One of its founders, and its main theoretician, was Charles Maurras, still a major reference today for the far right (and beyond), for its representatives or sympathisers, such as Renaud Camus and his oft-debated theory of “Le grand remplacement”, regularly quoted by the Rassemblement National and far right professional polemicists such as Éric Zemmour (you may have heard or read the adjective “Maurrassien”. Britannica: Charles Maurras, 1868-1952, French writer and political theorist, major intellectual influence in early 20th-century Europe whose “integral nationalism” anticipated some of the ideas of fascism).
In his seminal 1994 book Une jeunesse française. François Mitterrand, 1934-1947 (A French Youth: Francois Mitterrand 1934-1947), on F. Mitterrand’s shady past in the 1930s and during WWII, the investigative journalist Pierre Péan (who sadly passed away 2 years ago) established that François Mitterrand had “robust sympathies” for Action Française in the mid-1930s, when he was a young law student in Paris, when he’d gone to study from his native Charente department. Mitterrand also befriended members of the violent far-right anti-Semitic group La Cagoule, although there’s no evidence of Mitterrand took part in violent action, he even saved some Jewish friends from being beaten up with the Cagoule thugs, one of them, Georges Dayan, later a politician, became his friend).
While Mitterrand never belonged to Action Française as far as we know, he did go to a couple of anti-Republican marches organised by them (notably an infamous anti-foreigner and anti-Semitic series of demonstrations and strikes in Parisian and provincial universities in February 1935 called "manifestations et grèves contre « l’invasion métèque »",). Pierre Péan dug up a couple of photos as evidence, Mitterrand gave vague explanations as to his presence that day, unconvincingly claiming that “he didn’t really know what the marches were for”.
Mitterrand however did belong to the Croix-de-Feu movement, an organisation then mainly made up of nationalist WWI veterans, which he joined in 1934, aged 18, on his arrival in Paris from his native Charente department, where he had received a bourgeois, staunchly Catholic, anti-German and “anti-Bolchévik” education and grew up in the cult of Pétain (as the Hero of WWI).
Mitterrand, who cooperated with Pierre Péan in the writing of this biographical study (released in 1994) and gave Péan access to vital personal archives, was terminally ill by then and knew that the end was nigh. According to his proches he wanted to “se libérer d’un poids”, to free his mind from the weight of that past, in particular his murky role under Vichy France (he’s repeatedly made the dubious claim that he was merely what’s been called a “Vichysto-Résistant” – on the topic, I recommend the book “Les vichysto-résistants de 1940 à nos jours”, written by WWII historian Bénédicte Vergez-Chaignon) and the toxic friendships he kept after the war right up to his presidential time, chiefly René Bousquet.