Ahh, moved to a different thread. Sorry about the incorrect placement! Newbie mistake.
Right after I posted this thread, I got an email about the Peugeot. He said he has someone coming to look at it Saturday, and if the deal falls through, he'd let me know.
To elaborate more on the breaks, they didn't seem misaligned or anything (but I'm a novice here, so I'll be the first to say I have no idea what I'm really talking about), they just felt sorta soft. Had to squeeze more/harder to get the same braking power compared to the front brakes. They still worked though, enough for me to feel safe riding it without addressing the issue, but obviously not ideal.
I looked to see if anything looked horribly wrong with the drivetrain, but didn't see anything major. The entire assembly could definitely use a nice cleaning and then probably a good lube after, but the bike rode very smoothly. I was in my local bike shop earlier today trying some new road bikes, and it felt very comparable. Surprisingly so for the price difference.
The Peugeot is somewhere around 3 lbs heavier according to the spec sheets, but that doesn't concern me too much. Also, the C&V value of the Peugeot makes no difference to me. I just want something that will hopefully last me long enough to feel justified in getting a new bike eventually, knowing that it is an activity I enjoy and will stick with. I will see if I can barter with the Trek down to $150. If so, I will definitely take it. We will wait and see if the Peugeot sells as well. If it does, then it looks like the decision is made for me! Hahahaha
Thanks for all the help so far!