An M2 brane is coupled to the C3 field of SUGRA. And as you all know, a wrapped M2 brane gives us the fundamental string.
My question is, does the wrapped M2 brane (fundamental string) still couple to the C3 field to give us the strings electric charge?
In M-theory, the M2 brane couples to the $C_3$ field. The way this coupling is realized is by integrating $C_3$ over the M2.
Now if you compactify on a circle, and if the M2 wraps this circle, then it means one "leg" of the $C_3$ field it couples to is also along the circle. So in the effective 10 dimension theory you obtain by making the circle small, the M2 loses a dimension and becomes a fundamental string, and the $C_3$ becomes a 2-form in type IIA string theory. This two-form is the $B_2$ Kalb-Ramond form. And indeed you know that the fundamental string couples to the B-field in string theory.
This is the answer to your question, the fundamental string couples to the $B_2$ field, that is a dimensional reduction of the $C_3$.
Note that an M2 that does not wrap the circle becomes a D2, and this one still couples to the $C_3$ field.
