I have no answer for you. But interesting question.
I suspect you will have little luck at this unless you find a programmer that has actually done this sort of conversion. Check a local nursing home.
The time frame here is almost mind boggling.
Fortran IV was first released in 1962. 49 Years ago. Are your parents that old?
Fortran 77 came out in...surprise... 1977. 34 years ago. Your parents could easily be younger than that.
There have been a number of releases of Fortran since then, the last being 2008. You might have kids that are younger than that.
I suspect there were tools at one time to do this sort of conversion. But they probably don't run on any OS you own, or could own today.
Which takes me back to my original statement that you need to find someone who had at least been born back then, and let them apply their knowledge to doing a conversion. Expensive would be my guess.
Or, you find someone who can at least read that code, understand what it does, and have them rewrite it in a modern programming language. ( Fortran 2008 wouldn't be my first choice, but it might be the shortest path). Again...probably expensive.
If you do find a magic bullet solution to this...send me an email and tell me what it was. I always find it interesting when old code resurfaces after decades, and how people solve the problem.
Also: You might try asking this on Stack Overflow (second link). You are more likely to find people who have actually been there...done that than you will ever find on YA! But it's still a long shot, I suspect.