This is a good question. I cannot explain the time signature, but I am certain that it is a time signature. As evidence against the hypothesis that it is somehow a part of the repeat sign, note the last movement of the piece, which has repeats, but lacks the sign in question.
Note also the fact that the c-slash time signature is reintroduced at the end of the second section, which is why the unexplained time signature must be included after the final repeat sign as well as after the first repeat sign. The reintroduction of c-slash can be seen on the second page of the first violin part, at the end of the tenth staff. There is also a fermata on the first note of this measure, but it is difficult to see in this part because it is squeezed between the f' on that staff and the c''' on the staff below.
This is a natural manifestation of the French overture form, which typically begins with a slow stately section with dotted rhythms, followed by a faster fugato section. Anyone familiar with Handel's overtures knows that there is normally a brief return to the stately tempo at the end of the movement; here the road map is slightly different, such that the fugato section is followed by a return to the stately material and is then repeated without returning to the stately material.
Back to the symbol in question, I would note that its form is rather different from that of the numeral 2 written at the top of the Violin 2, Oboe 2, and Horn 2 parts, as well as the 2/4 time signature of the Andante Air. Of course, that doesn't exclude the possibility of the symbol in question nonetheless being derived from the numeral 2.
From the context, then, we can infer that the symbol implies a faster tempo. I suspect that the c-slash section is probably actually in 4/4, not 2/2, given the norms of the French overture form (The standardization of c-slash to mean 2/2 came later; for example, in Bach's Mass in B minor, the second Kyrie is in c-slash meter but has four half notes per measure.)
The meaning of the c-slash time signature for measures with four quarter notes could perhaps be established with more certainty with more knowledge about when these parts were prepared and by whom, and with some comparative study of Fasch's other overtures. If the stately section is indeed in a four-beat meter, it's reasonable to infer that the 2-slash means two beats per bar instead of four.