When the military woke up again in 62 in Algiers, De Gaulle crushed them.
You got it reversed.
Additionally, during the 1958 coup itself he did basically give his support for it in the sense that he explicitly said he was "ready to assume the powers of the republic" if asked for (which is what the leaders of the coup demanded be done).
Massu, who had gained prominence and authority when he ruthlessly suppressed Algerian militants, famously declared that unless de Gaulle was returned to power, the French Army would openly revolt.
> When the military woke up again in 62 in Algiers, De Gaulle crushed them.
Because then, the coup was directed against him!
Rene Coty himself said he would resigned if the national assembly didn't pick him as a prime minister.
Then the national assembly vote him with a huge majority margin.
And finally, he wins the november election in a landslide.
So if a coup means that you get power by following all the rules and the decorum and win the election, then the term "coup" does not mean anything.