If you search the internet, there are TONS of articles on bicycle tire rolling resistance. Conventional/historical thought was always "narrower is faster", but modern science (and modern tire materials) are demonstrating that's not necessarily true. It's a pretty complex science.
That's a good video that I recommend watching. It's primarily about tire
pressure rather than
size, but there is a lot of great discussion included there from someone who used to work with professional cyclists on finding the optimal tire pressure for them. He talks about the material of the tire (and its relationship with rolling resistance) and how to find the right tire pressure
for you. Hint: there is not a magic formula, and the "max pressure" on the sidewall is very likely not the one to use.
You asked about going narrower, and you absolutely can (it'll still fit fine in the fork!), but I would recommend changing the tire type to something a little nicer. Trek's stock tires are usually pretty inexpensive (and often come with a thick puncture-protection layer, which really slows the tire down). I bet the Continental Speed Rides I have on one of my bikes, that are labeled 42mm and are actually about 38mm installed on the rims, have less rolling resistance than the stock 35mm tires on your FX. Narrower tires designed for speed are usually much lighter than your stock tires and will also be built better. These are good things -- but you don't have to go narrower to find those attributes -- you can buy light, high quality tires in your stock size (and even larger).