I don’t think there is a connection between the language a compiler is written in and how fast the resulting programs are. If a Fortran program does not follow the syntax rules of C++ it is not a C++ program, regardless of the compiler implementation language.
I have thought about whether Fortran is a subset of C (or the reverse), but the idea has to do with Fortran/C interoperability. If any standard-conforming C function can be called from a Fortran program, without a speed penalty, and if all platforms with Fortran compilers also have C compilers, maybe one could say that Fortran contains a C subset with distinct rules.