you have to texture your object in C4D, then after importing your model into unity import your texture too, select your model, not the parent but the actual model that has the MeshFilter attached and expand the material - the last component in the inspector, then drag and drop your texture on the texture slot. should do it.
EDIT: UV map is exported together with the object by default in both Maya and 3DsMax, I’m pretty sure C4D does the same.