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.