[1] https://en.wikipedia.org/wiki/Charles_de_Gaulle#1958:_Collap...
There was indeed a coup but De Gaulle became prime minister and was given emergency power for six months by the national assembly all according to the Constitution of the fourth republic.
The coup of 1958 didn't happen in metropolitan France. It was lead by generals in Algeria. It certainly helped the decision of calling De Gaulle back to power but "through a coup" is stretching it.
The new constitution was then enacted by a referendum, new election called and De Gaulle was elected again.
By the way, it's hardly not taught. That's part of the official curriculum for the class of première (at least for L and ES).
As a side note, Mitterrand used to call the fifth republic constitution "the permanent coup". That didn't stop him from using the large power it gives to the executive when he became president.
The reason it isn't talked about very much outside the communist party is because it isn't nearly as controversial as you suggest.