The number of 25 wheels was of the M1777 version of Gribeauval when he regained control of the French Artillery. In 1775, Valliere Junior instructed the casting new Swedish 4-pdr, garrison guns and siege guns. These did not have the mouldings characteristic of the M1732 Valliere pieces however the dimensions were retained. [Note: The meaning of system used is upon the material and not the men.]
In 1777, Gribeauval absorbed this into his system as he only had produced the Field Artillery. Interestingly the Swedish 4-pdr was a infantry battalion gun so often ignored by the artillery. They are present in D'Urtubie.
In 1784, Manson became commander of the Corps Royal of Colonial Artillery. He redesigned the garrison carriages, designed the Manson M1786 iron guns and introduced the elevating screw to the siege artillery [assisted by Rostaing]. In addition he replaced the wheels on the Gribeauval Garrison Carriages with the same as that calibre for Field Guns or the 12-pdr wheel for the 16- and 24-pdr. This was a significant rationalisation. If you wish to look at a rationalised "Gribeauval" System then you should look at the M1800 Manson System of Bavaria.
The Siege, Garrison and Coast Artillery were the same as inherited from the 7YW with cheaper gun barrels as they were easier to cast and finish. It was not until 1786 that there was reform of these and you will find that Gribeauval was mot involved in this change as it was under the control of Manson. He died in 1789. The naming of the system is interesting and political. As he had conveniently died before he had to choose sides in the Revolution. He was neutral to the revolutionaries and royalists.
This is explained in the introduction to French Artillery of 1824. I can send you a copy of this but I know your bandwidth is limited. This is how far we got with the story in 2008 but much has been put together subsequently.
Rosen is an interesting read and seems to have come to the same conclusion as most of us here. France was bankrupt and lurched from one crisis to another. It is interesting to match the changes in the system to the date of the crisis.
In summary, there were so many vehicles and wheels because the French did not have the money to replace them. There was only a Gribeauval Field Artillery system so we should only count these wheels.
- Limber wheel, caisson back wheel, forge wheels, 4-pdr, 8-pdr, 12-pdr, Rostaing Gun, Swedish 4-pdr (?), three mountain gun wheels at least.
That I think makes it 10-11 wheels compared to the British 2 with an additional one for the mountain guns, M1800 Bavarian had three wheels, M1768 Prussian had four wheels. I could go on. These nations had abandomed the number of calibres to make a wheel about 1770 looking at the lessens from the 7YW and the AWI. It is a complex area defining precisely the wheels for the French as the diameters may be the same but they may be Light, Medium or Heavy.
The AnXI was the first integrated system for France since Valliere M1732 valliant attempt to restrict calibres. It failed in 1808 through lack of money. Napoleon invaded Spain etc... The French literature is very quiet upon the subject as in 1815 the royalists came to power.