The signature of your readFile is wrong.
void readFile(char fileName);
readFile is function that expects a single character, not a string. *argv[i]
returns the first letter of the string pointed to by argv[i].
void readFile(const char *fileName)
{
    FILE* file;
    int c; // getc returns an int
    file = fopen(fileName, "r");
    // always check for errors
    if(file == NULL)
        return;
    do {
        c = getc(file);
        printf("%c", c);
        if (!isalpha(c)) {
            printf("\n");
        }
    } while (c != EOF);
    fclose(file); // do not forget to close your streams.
}
Note here that your do-while-loop is wrong, because you should check first
whether c is EOF. If it isn't then you can print it. It should be:
while((c = getc(file)) != EOF)
{
    putc(c, stdout); // equivalent to printf("%c", c)
    if(!isalpha(c))
        puts("");  // equivalent to printf("\n");
}
Then you can call it like this:
int main(const int argc, char *argv[])
{
    int status = 0;
    for (int i = 1; i < argc; i++) {
        readFile(argv[i]);
    }
    exit(status);
}
Also note that getc returns a int, not a char, so the c variable must be
an int.
man fgets
#include <stdio.h>
int getc(FILE *stream);
DESCRIPTION
getc() is equivalent to fgetc() except that it may be implemented as a macro which evaluates stream more than once.
RETURN VALUE
fgetc(), getc() and getchar() return the character read as an unsigned char cast to an int or EOF on end of file or error.
See also this explanation