France is part of the Euro, and it's pretty much the Germans who decide when new Euros get printed. They haven't proven sympathetic to the idea of printing many recently.
There's a reason central bankers are always so concerned with anchoring expectations. In deciding how much money to hold onto, people and businesses make a trade off between liquidity and the cost inflation imposes on them of holding a given quantity of money. But if people's expectations regarding future inflation change, that tradeoff changes in a positive feedback cycle. If people expect more inflation then they'll want to hold less money than otherwise and in most cases this will cause more inflation[1]. If people expect less inflation than previously they'll now want to hold more money, causing further deflation.
Now, inflation expectations have clearly come unanchored because the GDP deflater, the measure of inflation most relevant to this particular effect, has been stuck closer to 1% than 2% since the financial crisis and the price spread between inflation protected and normal bonds means that the people who hold most of the M1 think this is likely to continue.
These effects are both self-limiting, the desire for liquidity isn't that strong so we only saw an 11% growth in the money supply despite inflation falling by 30%. And the inflationary spiral will quickly (but painfully) stall out if the central bank doesn't keep printing money to match demand.
Which is to say that sure, there's more cash floating around, but it's not just washing around it's being stored in people's pockets. It might be liable to cause excess inflation if the ECB ever manages to convince people that it will be able to hit its targets in the future, but it's not particularly benefiting France at the moment.
[1] In the mainstream economics sense of a rise in the price level, not the odd Austrian school definition.
