When considering character data, things are a bit more complicated in that the hardware does not impose a meaning on a given bit pattern. It is the operating system that does that. The character codes that are in common use are the ASCII collating sequence and the EBCDIC collating sequence. EBCDIC is only used by IBM mainframe and minicomputers (and their clones), but there are a lot of IBM computers around. (The IBM PC does not use EBCDIC.) Again it would be rather perverse if, on a given computer, FORTRAN and C used a different representation of characters, so that is not really worth worrying about. What certainly is worth paying attention to is the possibility that any given program may be run on several different computers, some using ASCII characters and some using EBCDIC. That is not a concern that is particular to mixed language programming though.
An important point about character data is that they are stored differently in FORTRAN and C. FORTRAN stores character data as a fixed-length string padded with trailing blanks whereas C stores character data as a variable-length, null-terminated string. The difference is standardized, so it does not lead to problems with portability, but it is something that will involve extra work when passing character data between routines written in different languages.
CNF and F77 Mixed Language Programming -- FORTRAN and C