The statement wasn't about the withdrawal of the US nuclear umbrella, it was about the use of those weapons as a first response should the Soviet Union invade Western Europe.
De Gaulle's argument was not that the US should withdraw nuclear weapons, it was that by softening the former hardline of nuclear response, it would make the Russians* believe the nuclear option would not be used to prevent aggression on their part.
De Gaulle believed that the threat of nuclear destruction was so overpowering as to encourage those involved in Europe to actively avoid another war. By toning down the nuclear deterence, it would, in his view, allow events that could lead to another war in Europe.
* de Gaulle typically referred to the Soviets as the Russians, probably because he saw them as the real power of the Soviet Union.
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