My (very brief) reading of the situation inclined me to belief that the coup was against de Gaulle not being harder on the communists and creeping socialism in Europe in general, with the decolonization efforts merely a proxy issue
Not exactly. While the officers involved in the coup were staunch anticommunists (many of them fought in Indochina), the primary reason for the coup was indeed the perspective of Algerian independance and De Gaulle's policy in favour of such an outcome. Among the high-ranking putschists, the coup was motivated by the feeling of betrayal, since they supported De Gaulle's coup in 1958 to keep Algeria, the refusal of the loss of the French Empire and of another defeat (not that Gen. Jouhaud was born in Algeria) and, true, the fear that Algeria would become a springboard for Soviet expansion in Western Med, not to mention the support for and from the Pied-Noir colony . However, many junior officers and the majority of the civilian putschists (especially in France proper) were inspired both by colonialism and far-right political ideology (from national-catholicism to neo-fascism). Note that a majority of officers serving in elite units were greatly inspired by the counter-insurgency doctrine which has been developped by French strategists after Indochina (and inspired US tactics in Vietnam and, after, in Iraq, as well as the 1970's dirty wars in South America, but that's another story).
I think that the dominance of the power of counter-insurgency doctrine (or "counter-revolutionary war") would have prevented the Generals from seizing the Bomb. The French strategic dissuasion doctrine proposed by Gen. Ailleret was, at the time, shared by few officers (ableit supported by De Gaulle and the Government), most of the Generals believing in more conventional tactics (basically using infantry and armour on a reformed German-like tactics to defeat Soviet armies, backed by the US strategic power) or in counter-insurgency. The Bomb itself was seen as a misuse of crucial ressources and a tool of poor military efficiency for the French army. That doctrinal mistake led the putschists to ignore the potential asset of disrupting op. Gerboise. To sum it up, the Generals would have been as capable of using the Gerboise bomb for their benefit as an octogenary would be at ease with programming a DVD recorder, if you see what I mean

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