Thank you everyone for the advice! I really appreciate it--I just wanted to say that I understand that I am extremely lucky to even be in this dilemma (this is basically a #firstworldproblems thread). I want to try to spend money wisely.
I think at this point I am going to try to do Paris for cheaper, and then also buy something preloved--maybe from Paris (which would be awesome), maybe just from eBay.
I also wanted to update on the numbers, in case anyone was reading this for reference--the $2500 for economy fare, round trip was quoted to me by the major aggregator sites (kayak, expedia, travelocity, etc). However, oddly enough the fares were MUCH cheaper directly from the airline carriers. All prices in USD.
For example, I looked up an arbitrary selection of airlines:
Air France: cheapest round trip economy around $1500
British Airways: cheapest RT economy class around $1600-1700
Delta Airlines: cheapest RT economy around $1500-1600
United Airlines: cheapest RT economy around $1500-1600
NONE of these websites gave me prices over $2300, and I used the exact same parameters (date, # of people, economy class) as I did on the aggregator sites. So just a tip--search the individual airlines as well!
Hotel prices for mid-tier centrally located chains are still around $200-300, but I'm thinking of renting an apartment instead, and a 7-day rental for a VERY nice apartment is 720 euros. So about 1000 usd. That's less than $150 a night! Airbnb also seems to be an options--I've found decent-looking apartments for $80-100 per night.
So it looks like $3000-5000 was definitely overestimated by me for a 5-10 day trip to Paris. I'm very relieved

I did a quick eBay search for a basic, tri-tone Cartier trinity ring, and the prices looked fair (although not sure about authenticity!)
It seems that this is less of a dilemma than I thought. Although I think I'm pretty set in my decision now, if anyone still has thoughts I would love to hear them! I find it really interesting to hear from a lot of people about how they allocate their finances.