Preprocessor directives like #include are just doing some textual substitution (see the documentation of GNU cpp inside GCC). It can occur at any place (outside of comments and string literals).
However, a #include should have its # as the first non-blank character of its line. So you’ll code
float h[N] = {
#include "f1.h"
};
The original question did not have #include on its own line, so had wrong code.
It is not normal practice, but it is permitted practice. In that case, I would suggest using some other extension than .h e.g. use #include "f1.def" or #include "f1.data" …
Ask your compiler to show you the preprocessed form. With GCC compile with gcc -C -E -Wall yoursource.c > yoursource.i and look with an editor or a pager into the generated yoursource.i
I actually prefer to have such data in its own source file. So I would instead suggest to generate a self-contained h-data.c file using e.g. some tool like GNU awk (so file h-data.c would start with const float h[345] = { and end with };…)
And if it is a constant data, better declare it const float h[] (so it could sit in read-only segment like .rodata on Linux). Also, if the embedded data is big, the compiler might take time to (uselessly) optimize it (then you could compile your h-data.c quickly without optimizations).