There was a pretty popular vocal group around this time called Les Quatres Barbus . That does translate as The Four Bearded Ones. Definitely can not imagine them having anything to do with targeting OAS members for de Gaule!

So, since i somehow managed to baffle the learned /r/AskHistorians, I went off to do some research on my own.

Though I am from a part-french familly, politics meant that the whole 60's Algeria thing is never mentioned at home.

I went hunting for decent works on the subject and i found a few. La fabrique des Barbouzes by Jean Pierre Bat and Barbouze du Géneral by Pierre Lemarchand were rather usefull, although since the second one is autobiographical, it should be taken with a few pounds of salt.

To start at the begining, the word Barbouze comes from the french argot (slang, very detailed, like cockney slang without the rhymes) and refers to employees of France's clandestine services source as well as less 'official' helpers, who would be called in to do the dirty work.

In the late 50's and 60's, france was undergoing decolonisation and the main fears of the governement were that the former colonies would turn 'red' and that french right wing military groups would oppose (violently) the giving up of the colonies. The official secret services could only do so much, as their oversight prohibited direct actions. This led to the creation of many small, illegal and ultra violent terror groups, collectively known as Barbouzes ( source for a list)

I'm not going to go into all the details of the existance and interaction of those groups as that would require a book but i'll just note that most of them were allegedly non-governemental but recieved funding from state black fund but rarely equipement. That came from spoils taken from the FLN (algerian independence group) by the french army and then handed over to their Barbouze friends.

Originally intended to kill communist and populist leaders in soon to be former colonies, the Barbouzes extended their purview when the government made heavy use of them against the OAS (organisation armée secrète) which was a right wing paramillitary organisation which sought to overthrow the elected french governement. The allegations of torture against the various barbouze groups were many, but never prosecuted as they acted with the unoffical blessing of the highest ranks of government. ( source )

In 1962, it was decided to bring home all barbouze survivors. That accounted for less than half of the original fighters (numbers vary but a consensus say 400 were sent and 200 came home.). They had killed, tortured and dissapeared almost all of the active cadres of the OAS and the various socialist/communist groups in Algeria.

This was some very depressing research, as I also found out no one was ever prosecuted for these crimes against humanity. Sorry all of the sources are in french, but in this case i thought it better to stick with original sources.

EDIT: this is my first real attempt at a top level answer (albeit to my own question) so please all critique is welcome and a real answer from an actual historian would be great. I'll try to answer followup question as best I can