>I know it’s common for massive projects to use Fortran in order to train NN.

It is definitely not common. Yes, Fortran is used in scientific computation applications due to efficient and well tested linear algebra libraries and other numerical computing legacy code.

Fortran code is or can be used under-the-hood of higher level libraries / languages, such as Numpy for Python or Matlab. Even PyTorch uses LAPACK for linear algebra computations when running on the CPU. In this sense, yes, Fortran code is used, indirectly for training NNs. But using Fortran to actually implement a NN model and train it is virtually unheard of, as far as I know.

Maybe having a look at LAPACK will give you more insight.