You can use
fseek(file, 0, SEEK_END)
If you try to read from it, you'll get your second EOF.
EDIT:
Reading the reference more carefully: "Library implementations are allowed to not meaningfully support SEEK_END (therefore, code using it has no real standard portability)."
I guess your solution is the best one in terms of portability.
Just be careful with fseek (as a note because this is not your case I believe): Using fseek to backtrack