Well the Bank of England was semi-independent and had been successful in repairing/maintaining the British economy, so would it be so odd for one or several French economists to use their rival's relative success as en example of what could work in France?
The Bank of England had no obvious maintenance or repair role in the economy prior to the middle of the 19th century. At the time, it was thought of as a purely private entity with purely private interests which had a monopoly on government credit, whose only public obligation was being willing to extend that credit at the government's will (in exchange for certain privileges which eventually led to its monopoly on note issue).
The idea of central banks as economic regulators only really reached anything like maturity in the 20th century and only entered into
practice about a quarter of the way through that. Before that, they were government creditors with privileges, with some vague but increasingly, over time, distinct idea that their management of the money supply must be better than what private banks could do because reasons (which also happened to be highly convenient for the people making those decisions, since a monopoly central bank is much more capable of extending credit to the government than a non-monopoly central bank).
The prime reason a French monarch is going to create a new Bank of France is going to be for reasons of public finance. The problem is that it's going to be VERY hard to get its notes to circulate in France with the memory the Mississippi crash still relatively fresh. The French monarchy would actually have had a lot of trouble getting legal tender laws to 'stick' in the French countryside and the ability to keep notes in circulation is how banks like that back then made money. Without that ability, a new Bank of France is going to have limited ability to extend credit to the monarchy, and thus limited utility to that monarch.
There's a reason that it's an extremely rare case (I cannot think of one off the top of my head, and this is something of my area of specialty) where a note-issuing central bank
precedes private issuers. It's really, really hard to get people used to using money with heft and a sense of solidity-in-hand to switch to flimsy paper notes. There has to be a large degree of comfort in an extended market and trust in the institutions issuing those notes that is hard to come by in the fragmented economy of the ancien regime.