The Prussian major of artillery J. C. Plümicke gives in his handbook for Prussian artillery officers, 2 vol., Berlin 1820, the following rule (vol. 2, p. 345, § 469):
The minimum number of artillery men necessary for a siege is calculated from the highest number of guns which can be employed after the completion of the second parallel. This number will be multiplied by 10, as in average 2 men per gun/howitzer/mortar are needed, which will make 6 men in three shifts. The other 4 men are replacements for ill, wounded etc., and are used as workers. In order to serve the guns, and as workes, the equal number of infantrymen wil be attached to the artillery. Experience has shown that even a lower number of artillerymen can also be sufficient.
I don't know whether British or French artillery had generally more artillerymen a their disposition.