What I won't discuss:
I don't intend to write on all potential actions open to France. If you assume that even war is a plausible response, then you could mention an infinite number of other options.
Wrong basic assumption:
Your basic assumption The adoption of a new currency would really hurt France's financial power is wrong. Many people would perceive the disappearance of the CFA Franc as another symbol for the decline of French influence in the so-called Francafrique. However, the direct economic impact would be small, almost negligible. The most tangible benefit for France is the obligation of CFA Franc members to deposit 50 % of their national reserve money in the French treasury. This sounds like a great advantage, but in practice it's of no great importance (BBC article, already cited in a related question):
In December 2017, the central banks of West Africa and Central Africa had €5bn (£4.3bn) and €3.9bn in the French treasury, respectively.
This is a small amount compared with total French public debt, which stood at about €2.2trillion in 2017.
How much does France possibly gain? France pays 0.75 per cent of interest on the deposited money. You can calculate how much more it would have to pay, if it had to obtain the same amount of money by selling sovereign bonds of a certain maturity. At current interest rates - even if the deposits were several times larger - there wouldn't be any reason for France to care, much less to feel threatened by the abolition of the CFA Franc.
The loss of the peg between Euro (or previously French Franc) and the Franc CFA could still have real economic consequences. If the currency risk increases, this could have a negative impact on trade, investment decisions, savings of African citizens in France or Europe (and theoretically vice-versa). However, if you ignore its closer economic ties to the region, France is as much concerned as any other country in the Euro zone
What France will do:
French diplomats will certainly continue to promote the CFA Franc as guarantor of economic stability (absence of monetary crises, like those in Argentina or Zimbabwe) and raise questions about the prospects of a new currency and its advantages.
Currency pegs never a good thing?
Mainly as a response to a user comment to another proposed answer:
This answer is extremely simplistic in many ways. Importantly, France gave up independent monetary policy a long time ago. It's true that a currency pegged to that of a larger economic area is not a good thing but that's exactly the situation France is now with respect to Germany. The CFA Franc hardly benefits the country and is mostly a symbolic curiosity.
I consider this answer itself extremely simplistic. It's true that a currency pegged to that of a larger economic area is not a good thing is wrong. It may be correct in a specific case, but it's not unquestionably true.
There is a strong incentive for smaller economies to peg their currency to another currency belonging to a larger economy, whether the US Dollar, French Franc (CFA Franc!), Deutsche Mark (e.g., Austria, Bulgaria), Euro or others (see List of circulating fixed exchange rate currencies). Historically, countries had their currency pegged to gold or silver, which was equally outside of control by "monetary policy". Many countries voluntarily maintain their currency pegged to that of other countries, notwithstanding Argentina or other examples. Even now, the CFA Franc member countries don't want to create local, national money - but a new supranational currency outside of their control!