I'm not an historian and english is not my native langage but I'll give you my thoughts as a French deeply interested in my country's history (and in particular on everything related to De Gaulle).
I believe that "Socialist revolution" is not the concept you are looking for.
What happened in 1968 is that a "boring" traditionnal society was questionned by the students born during the baby-boom. That generation didn't know the war and wanted a more free society (think about Woodstock in 1969).
The socialist ideas have always been strong in France so this willing of a more free society was accompanied with some left-wing revendications. A lot of left-wing militants tried to take advantage of this, but they were mostly split : the actual "socialist" (the French Communist Party, that was defending the USSR) tried to use the students rebellion for their purpose but a lot of students, even if they had a left-wing sentiment, were not really USSR lovers (Daniel Cohn-Bendit, a leading figure of the riot, was hated by the communist and vice-versa). The Communist Party achieved to made workers to participate at the rebellion in the end and that's why the Grenelle agreements, which grant a lot of new rights to the workers, have been signed at the end of the riot : https://en.wikipedia.org/wiki/Grenelle_agreements. But these actual revendications were far from achieving a "socialist revolution". France was doing good in an economical point of view (almost everyone had a work, after the WW2 a lot of agreements granted a lot of rights to the workers etc.).
Overall, the sentiment that leaded to this big riot was more a willing of change from the young parisian people, tired of this "General de Gaulle" which represented the "old-school" France.
I would say to answer directly to your question that France was far from a socialist revolution around 1968. In June 1968, the legislative elections was won by the political party supporting de Gaulle, and in 1969, Georges Pompidou, who you could consider as the sucessor of de Gaulle (although Pompidou is more controversial and sometime described as an politician opportunist) was elected.
Workers had what they want with the Grenelle Agreements and young people, without giving up their will of a "general dream" (which is a pun from the "general strike" watchword because in french we say "Grève Générale" and "Rêve Général"), went back to the university slowly but surely...
Many have asserted this as well, but the simple answer is: 'not really that close,' but the reality is slightly more complicated.
A brief look into the historiography shows a hesitancy to use the term "revolution." Historians often use the more euphemistic "events" as a reference to the fact that something happened but without major political upheaval. Raymond Aron's critical indictment La Revolution Introuvable, which came out mere months after the crisis, coined this terminology. Even Herbert Marcuse, who students cited as a major influence in their 'revolutionary' philosophy, explicitly condemned using the term revolution.
More recently, historians like Kristin Ross and Julian Bourg have argued against the inevitability of these events and also of their social impact, with Bourg in particular arguing that popular conception of Mai 68 is almost a lieu de mémoire, borrowing from Pierre Nora's conception of French history as a confrontation between memory and actual events.
In May 68, students and socialists (the PSU, FGDS, and Communist PCF) were "tired" of De Gaulle in many ways. The runoff presidential election forced in 1965 between Mitterand and De Gaulle, which had previously been unthinkable, showed cracks in De Gaulle's dominance in 5th Republic politics. There are many background events, from anger over the Vietnam War, to lingering tension from the Algerian Crisis of 1962, to the outbreak of the Prague Spring, that helped aggravate these anti-Gaullist feelings.
The events kicked off in May after protests began in March at Nanterre University, but the barricades and the mass strike only lasted about a month. The unions (especially the CFDT and CGT) made deals with the government to resume work, and students went back to class, afraid of missing exams, among other things.
De Gaulle, for his part, traveled into Germany during the protests to prepare a potential military counteraction, but it never came to this. It's true that the events forced a new election, but the Gaullist coalition received an even greater majority of votes then they had in the previous elections in 1967. De Gaulle famously resigned after his attempted reforms failed in 1969, but it took an entire decade of gradually leftward-shifting elections before Mitterand and the socialists took power in 1981.
There's much more to it than this, but hopefully this is a helpful summary.
Further reading, and used sources:
Summaries and Chronologies:
Keith A. Reader, The May 1968 Events in France, 1993.
ed. Philippe Artieres and Michelle Zancarini-Fournel, 68, une histoire collective, 2008
Kristin Ross, May 68 and its Afterlives, 2002
Julian Bourg, From Revolution to Ethics, 2007
Anti-68
Raymond Aron, La revolution introuvable, 1968
Bernard Brown, Protest in Paris: Anatomy of a Revolt, 1974
Pro-68
Laurent Joffrin, Mai 68, Une histoire du mouvement, 1988
Alain Schnapp and Pierre Vidal-Niquet, The French Student Uprising, 1969 (English translation 1971)
Wasn't it a socialist revolution? An election was forced by activists wanting representation from socialists and communists. The economy ground to a halt. De Gaulle was ejected from the country. In the resulting election it was clear those political sentiments weren't the majority. My understanding is that '68 was also about some of the issues the counter culture movement was about in America, so cultural unrest as well as political. If your question is how close were they from physically taking control, I don't know.
I can't really speak to how close France was to revolution in 1968, but I thought I should point out that there are big debates about whether May 1968 was a socialist / Marxist revolution or not.
One of the most popular alternative views is that May 1968 marked a turning point away from class-based politics to what are called 'New Social Movements' (NSM) (Staricco 2012 has a good overview). In a nutshell (and grossly oversimplifying), NSM theories said that in late capitalism, class struggle becomes less important to political change while identity-based concerns (race, gender, sexuality etc.) become more important. Some of the evidence in favour of seeing May 1968 in this way includes the cross-class composition of the protests and the 'post-materialist' concerns of many of the protestors.
I personally don't agree with this approach, because I think it takes a much narrower view of Marxism than you'd find even in the works of people like Guy Debord, who were heavily involved in May 1968 (Chapter 1 of Barker et al.'s 'Marxism and Social Movements' outlines this critique pretty well if you're interested). But there's definitely controversy about whether May 1968 was socialist.
Sources:
Juan Ignacio Staricco, 'The French May and the roots of postmodern politics' (2012) 53:3 Rassegna Italiana di Sociologia 447.
Colin Barker, Laurence Cox, John Krinsky and Alf Gunvald Nilsen (eds), Marxism and Social Movements (Brill, 2013).
was this during the student riots etc?