I got my professional start as FORTRAN programmer for process control systems and simulations for Petrochemical, Oil & Gas, Food & Beverage, and Nuclear industry. /u/kjs3 answer provides direction on where to look for FORTRAN opportunities.
I believe environmental science, fluid dynamics, aerospace, nuclear, and geology still uses a lot of FORTRAN based back-end. Most of FORTRAN is tough to replace as, other than C, I haven't seen any language that can provide the scientific/mathematical computing libraries, for example numerical methods, that FORTRAN has.
Instead of thinking of refactoring legacy FORTRAN code, think of putting a new user/web interface in front of FORTRAN. There may be better opportunities on updating the 'user interaction' with FORTRAN based systems specially in simulations arena.
I don't think the FORTRAN comp will be anywhere close to COBOL comp. With FORTRAN, you are dealing with typically misson-critical applications rather than COBOL based business applications so there is much higher resistance and lower opportunity to show direct revenue/profit impact. A few times, I have been approached by vendors who have been trying to replace the FORTRAN based systems, I worked on, with their C based products. These vendors typically have balked on my contract rate expectations, that I get doing big data analytics.
Why not ask you dad for the FORTRAN based systems he used and talk to his industry connections for getting the feel for the demand. Your dad most probably will get lot more kick out of you trying to understand what he did. When I was working on a facility very similar to the one my dad used to work, he really got the kick out of understanding how things are changing.