It used to be that most scientist/engineers would learn Fortran, since much legacy code was written in Fortran. Now C/C++ has become a standard scientific language, and there is an emphasis on object-oriented language. It's probably helpful to have familiarity with both.
The broad area of application is now 'computational physics', or 'computational multiphysics', in which one attempts to simulate a broad range of physical phenomena over multiple time and length scales, from atoms to planet size, and larger, and picoseconds to billions of years, depending on the physical system being modeled.
The challenge is to understand the physical phenomena involved and the mathematical equations that describe the system in sufficient detail to allow a reliable or realistic prediction of the behavior.
See for example -
http://farside.ph.utexas.edu/teaching/329/329.pdf
There is a broad array of computational tools from which to choose:
http://prancer.physics.louisville.edu/astrowiki/index.php/Programming_for_Physics_and_Astronomy
In engineering, one would be concerned with movement, heat transfer, fluid flow, electric/magnetic fields (and currents), forces/stress, . . . .
To this end, there are numerous computational systems, e.g., Comsol, ANSYS, ABAQUS, . . . . The US DOE is supporting a system called MOOSE (based on C++).
Perhaps one should explore Python as well as exposure to C++ and Fortran.
https://en.wikipedia.org/wiki/Python_(programming_language)
http://www-personal.umich.edu/~mejn/computational-physics/
https://en.wikipedia.org/wiki/C++
https://en.wikipedia.org/wiki/Fortran
So one should explore 'computational physics' and/or 'numerical methods' with language as a qualifier, and see what various universities are teaching.
e.g.,
https://courses.physics.ucsd.edu/2017/Spring/physics142/Labs/FinalProject/NumMethods.pdf
https://www.uio.no/studier/emner/ma...Lecture_notes_and_literature/lectures2012.pdf
There are still plenty of legacy codes written in Fortran.