Well, you mentioned a richer France. That has impacts beyond just "What if France makes better decisions"?
France doesn't need to be richer, just better at finances. With the Glorious Revolution putting Dutch financial expertese into British hands the government was able to reorganise the Navy (see Samuel Pepys' diaries) and to build the largest factory in Europe (Portsmouth Dockyard) to support its navy. France didn't have this oportunity.
Without wishing to state the obvious Britain is much smaller than France, so the cost of gathering raw materials is less and could be done inland if necessary (such as the Dutch attacks on Chatham). When France needed to move materials between dockyards it HAD to use the sea (and was therefore vunerable to British attacks) as the road system in France made movement of large amounts of supplies imposible.
If France wants to match (or exceed) the RN it must:
1) Have the will to invest in the navy over the army (and therefore need secure borders);
2) Have the financial infrastructure to allow the outfitting of a navy and to support its lenght of time at sea;
3) Have a road system that allows easy access to all the dockyears from anywhere in France;
4) More oak forsts;
5) Formalised basic training for officers and men with promotion by merit as well as birth.
Or in otherwords if France wants to beat the Brits at sea it needs to become more British!