I'm afraid you need a 10-, or preferably 20-, year perspective, not a week.
About C compatiblity: Many C libraries use pointers in their interfaces. Interoperability is indeed defined by the Fortran 2003 standard, which I have used several times to wrap existing C libraries. However, much of the existing code is F90 only (some even F77...), and a vast majority of Fortran developers in the field are not familiar with even modules and other F90 features, let alone iso_c_binding in 2003.
Also, newer libraries tend to be C++ as well, which is more difficult (or at least more awkward) to wrap.
Finally the fact that groups like Facebook and google are writing their machine learning code in C++ shows that 1 they find it useful and 2 plenty performant. This kinda became a response to the comment above yours sorry.
If you don't feel like it, feel free to ignore.
My background is in QM, so I guess that's my bias showing through :)
Somewhere under http://www.archer.ac.uk, there's a summary of the time used by various codes on that UK "Tier 1" system.
New libraries are being written in C/C++, and maybe Python. This includes libraries that should form the foundation of the QM community (matrix/tensor and integral libraries). These are meant to take advantage of newer hardware and libraries which themselves are written in C/C++, and often in a way that is inaccessible from Fortran.
The old Fortran code will be around for a long time, but I don't know of any large-scale, serious efforts to develop new packages or major new functionality that are starting with Fortran.
(I'm not totally against Fortran - I just spend a week devloping in it. But I still much prefer C++ and Python)