My experience with Fortran is that it's easy to learn, clean (being highly modularized), and thus well suited to a non-programmer whose main concern is doing highly optimized numerical computations. Although equal optimization can be performed in c++, (even perhaps to a greater extent), it takes a lot of instrinsic understanding to achieve those level of optimizations. When it comes to matrix calculations, out-of-the box a Fortran compiler will normally out-perform a c++ compiler. I'd also add that Fortran has keywords that are specifically designed to help the programmer to squeeze more performance out of a numerical routine. C++ has this too, but not to the extent Fortran does.
Another advantage is that Fortran is not operating system or architecture specific. In other words the Fortran code you write on one operating system or architecture should easily port to another where there is a Fortran compiler.
Another advantage is that modern Fortran is normally backwards compatible with older code bases of Fortran. And the code base that has been built over the years in Fortran is huge and extremely sophisticated (being mostly done by scientists and mathematicians).
Also, personally, I really enjoyed the built-in file handling functions that allow one to read a data file and perform operations on it almost instantly. Many other built-in functions in Fortran are designed to allow this convenience. C++ offers mainly building blocks to do this and this requires a bit of sweating it out just to read a data file b/c you need to know something about delimiters (where Fortran allows you to specify the delimiter).
Beyond this I can't think of advantages. Most anything else would be string manipulations, or algorithmic based operations to which c++ as a language, and in general it's compilers, are better suited and most often will perform better. A good knowledgeable programmer will likely prefer c++ as she/he would understand how to optimize a numerical routine in a way that could likely perform better than a Fortran compiled routine. Additionally good reliable Fortran compilers are not as easy to come by as good reliable C++ compilers.