Does the front derailleur limit chain ring size? Does the front derailleur have limits to which size chain rings can be used? 

I have a groovy old 1988 Schwinn Prelude and for the most part it does just what I need. However there are some steep sections of excellent paths nearby that are a bit to much. Fitness is decidedly a factor ;) 

I currently have a 2x6, I assume stock parts but I cannot be sure. Chain rings are 52-40 and cassette is 14-28. The aggressive old style. There aren't many options for changing the cassette, but I was thinking perhaps I could put a compact or even a gravel/mtb chain ring set on. 

I use exclusively the 40t ring. I can count on one hand the number of times I've used the 52t. I mostly commute and go for leisure rides, so the racing set up is impractical. Can I simply switch the chain rings out for a 42-34 for example? Or will the front derailleur be unable to function properly?

The derailleur is mounted with a bolt on band so it is maybe possible to lower it on the seat tube slightly to accommodate the new rings.
As Criggie says front derailleurs have a maximum chainring difference and min and max tooth counts. the more modern a derailleur and shifter is the more important this is. With an old friction shifter you can probably push this quite a lot.

The bigger issue is the 'bolt circle diameter' on the chainrings and crank. It's probably wide enough to preclude a ring much smaller than 40 teeth, if you want a smaller ring you'll need to find an alternative crank.