Get a room somewhere and sleep.
I've done more than my share of those trips - that layover is tailor-made for getting a good bed and some sound shut-eye.
But Schipol - where I went through - had a hotel right in the airport. Best room I ever rented. And that was back when I was young and supposedly could take it...
I don't know what's at FRA, but you'll be spending your trip seeing the sights in Egypt and I'll bet you'll be downright worn out after getting up for a 3AMish flight.
And you imply your wife quite pregnant - she'll certainly appreciate the break.