There isn't the same level of embarassment as the level of involvement of French conscripts was extremely limited, and the "metropolitan French" casualties (i.e. the casualties born in the european part of France) were very limited. Domestic opposition to the continuation of our involvement in Indochina was either :

• based on a political opposition to colonial rule, sometimes related to early cold war alignments (for example the communist Party had a firm opposition to it, and historical relations with some of the vietnamese and cambodian insurgency leadership : for instance, Ho Chi Minh was a member of the French communist party when he lived in France). Opposition of the left-wing parties and the intellectual milieu of the time can be traced to such feelings (see the numerous interventions of Sartre, or the song "the deserter" by B. Vian)

• linked to budget issues, and a general feeling that it was not worth spending that much taxpayer money for far away territories bringing limited benefits to the Métropole. [As a French citizen and taxpayer, I found it indeed weird to travel in Laos on roads with the same type of roadsigns we have in rural France, suggesting that the French taxpayer was paying for building roads in the middle of nowhere in the mountains of Laos in the 1930s]. For example Jean-Pierre Rioux , based on work from Charles-Robert Ageron, Alain Ruscio and opinion polls of the time concludes that 75 % of the French population showed no interest in the conflict.

There was an extremely limited French population living in Indochina (mostly civil servants).

Soldiers fighting the vietnamese insurgency on the ground were, for a major share, from the "Union Française", i.e. recruited from the various african and asian colonies and protectorates, or from the Foreign legion (with a significant share of German/French Alsatian soldiers in it, who joined in after the end of WWII). [Edit : In Indochina, there was also a significant share of local troops recruited from mountain minorities (the "Montagnards", in French colonial parlance), that is Hmong, various Tai and other people, with historical defiance of the vietnamese majority. This practice, which was deep rooted in traditional colonial policy of opposing local peoples to maintain colonial dominance (and a British specialty as well) had repercussions in the american involvement when CIA (and others) tried using the Hmong and other Montagnards for counterinsurgency, in particular along the Ho-Chi-Minh trail. There is still some low key guerilla activity in the mountains from this (and signficant oppression of those peoples by the Vietnamese regime, as far as I understand it)]

As a conclusion, this war does not entail the same level of national trauma as the Vietnam War in the US. The people most attached to its memory are mostly former veterans and/or with personal military attachments and in the indochinese community in France. If you want to watch really good movies about this period, I would recommend the movies by Pierre Schoendorffer (who was a journalist there at the time embedded in the military, and took part in Dien Bien Phu) who made several major movies about this war : "Le crabe tambour", "La 317e section" and "Dien Bien Phu". [Edit : "Le Crabe-Tambour" and "L'honneur d'un capitaine" deal with the Algerian Insurgency : all of these movies show the typical mix of soldiers fighting in those conflicts, with a share of soldiers either recruited locally or from other colonies.]

Also, fun fact about the end of the Indochina war : traffic of opium products in the region was dominated by corsican expatriates in Saigon ; after the war, they reorganised their networks, and this became the "French Connection", which brought first opiates into the US (see the movie of the same name, for instance).

Our "national trauma" of the same time frame is more the Algerian Insurgency. Algeria was considered a part of France on the same level as metropolitan territory (from an administrative standpoint) and had an ethnically european population with full French citizenship numbering in the millions, who had to leave everything in 1962, sometimes after several generations of life in Algeria, and be "repatriated". The topic remains nationally divisive (for instance, it wasn't refered to as "Algerian war" but as "Algerian events" in official documentation and speeches, until the late 1990s). Right-wing movements that structured in opposition to the Algerian independence were some of the groups at the origin of the foundation of French modern far right (National Front, notably).