I'm no expert, and don't have time atm for any depth, but offhand I can tell you that the ideas and slogans of the Situationists were prominent in the uprising. So that's one thread you might be able to pull if you're interested in the ideological climate of that time.
It was generalized unrest against the right-wing Gaullist government. There were two big groupings of leftist protesters. The whole thing started over student occupation protests linked to other counterculture protests worldwide, and the trade union confederations joined in with sympathy strikes. De Gaulle, an authoritarian (and fascist-lite in my opinion), cracked down with the police and things got ugly.
The workers and unions in alliance with the French Communist Party, IMO, were proto-Eurocommunists, meaning they were groups that decided to focus on labor issues in Europe only without considering the third world or social justice. This ideology was a product of the Soviets' "Socialism in One Country" days in the Stalin era, and a reaction to a post-WWII shift in the communist world away from Marx's original plan to establish communism in Europe before the third world. They weren't all onboard with the free love and other social causes that the other group was espousing, but they jumped on the chance to advance their cause.
The student groups were following the lib-left and anarchist counterculture groups like the Situationists Cassandra mentioned and can explain better than me (IMO, anti-authoritarian Marxism with a heavy focus on the artistic flair needed to erode traditional institutions and spread their message- seriously guys, why not just follow Mao Zedong Thought?). Unlike the French Communist Party and the unions, which were nominally pro-Soviet and anti-Chinese, the libertarian socialists and anarchists actively criticized both the USSR and China. There's a picture of graffiti from the protests out there somewhere responding to Mao's quote- "let a hundred flowers blossom; let a hundred schools of thought contend"- with "let my flower bloom". They weren't old-style socialists who wanted to establish, I dunno, "the Workers' Republic of France" necessarily. They wanted social change.
The difference between the two was largely generational. The former group wanted to address economic inequalities, the latter group confronted all inequalities. I never understood May '68 either until I understood the history and ideologies of leftism. You can think of it as a big-tent anti-government movement like the Yellow Vests today.
