I have not done a census of the various libraries around, but all of the free finite element libraries in common use (deal.II, libmesh, and FEnICs come to mind first) are written in C++. I suspect Fluent and Abaqus are written in C (maybe Fortran?) but they are a bit older.

Trilinos is another C++ example, while PETSc and HYPRE are written in C.

My tentative conclusion from this is that newer projects tend to use C++ and slightly older projects use C.

Yes, there are things like ODEPACK, QUADPACK, and FFTPACK, but those are not under development anymore (as far as I know). The only widely used Fortran library still under development I can think of is LAPACK.

I did not count the occasional 'bespoke' code. There are still some Fortran applications in development for particular purposes (like MOM), but those are harder to survey.