What you say is that there is more demand for the Dollar. That does not change the fact that the price halves when the supply doubles.
Price = demand/supply.
Price = demand/supply.
But as I wrote. This is a controversial subject. And there are economists out there who will tell you that the special status of the US dollar makes no difference at all and this de Gaulle guy just was upset about losing some colonies.
Why? It would be quite odd. Certainly Japan has generated far more currency and debt over the last 35 years while inflation stayed low (and the relative value of Yen stayed high). I don't see any explanation for that here any more than the yearly gyrations of other currencies crypto or fiat.