There is of course a good question why exactly you'd like to create a new finite element library in 2015 when there are already excellent ones out there. There's also the question why you would want to use Fortran in 2015 when that's simply not any more what the community believes is the language to use for new projects.
But if you believe that you have good reasons for both of these questions, then it may be worthwhile looking into PLTMG -- the grandfather of all modern finite element libraries, and written in Fortran. As others have pointed out, PETSc also provides interfaces for Fortran and has finite element support built in.
There's also the question why you would want to use Fortran in 2015 when that's simply not any more what the community believes is the language to use for new projects.Really? There shouldn't be any doubt that optimized fortran programs will be computationally cheaper as compared to c++; papers show benchmarking. And fortran is still language of modern scientific programming. Many commercial finite element codes are still in fortran. – 343_458 Oct 02 '15 at 23:22