One thing I'd worry about is that this kind of pension may only work in a closed system. People not living in France may still purchase French assets for investment, just as they continue to purchase international assets for investment, which will still drive an increase in demand. That could incentivize French people to continue investment, in the absence of strict capital controls.

And yes, it is somewhat common! I think your second point is definitely part of the problem. As to your first, I think that looking at inflation in these terms requires looking at interest rates as well. When both inflation and interest rates are low, hoarding cash is highly incentivized. If inflation is low and interest is high, there is a large opportunity cost to holding cash rather than collecting interest via a mechanism directly tied to the cash (e.g. a bond). If both inflation and interest are high, it would probably be optimal to invest in assets that won't have their underlying value erode as they do with bonds.