As others have mentioned, miles are great when you either have a lot of flexibility with dates/location or are booking 9-12 months in advance.
We did a similar kind of trip last summer (SO had work trip, I was tagging along). I booked in Feb for a late june departure, and it was hard to find any tickets at all in and out of Europe (this was on United). I spent a ton of time looking at every possible combo of date/location on their website, and eventually found something so I could get to Europe and back for 60,000 miles.
For the first flight, I couldn't find anything out of my local airport. But there were tickets out of Phoenix, and I have a friend there, so I spent $80 on a one way to PHX, stayed with her for a couple of days, and then went flew to Europe. So maybe broaden your home airport search?
I ended up flying out of Paris, which was a <$100 flight from our destination, so I spent one day there and then flew back to the states. There are worse things than an extra day in Paris, and weirdly a friend ended up being there so I had dinner with her and it was great.
My SO flew in and out of our actual destination, and spent $1900 on his ticket. I had to spend about 200 extra for the extra flights to get me where we were going, but it was totally worth it, and the PHX Paris parts of my trip ended up being fun little bookends.
I will say that May is not yet peak travel season, so you should be able to get something cheaper. I was looking for tickets to France (both to Paris and to Bordeaux) in May/early June last year for my sister, and for early may there were tickets priced around $800 (this was in March that I was looking). So prices will probably go down, and you may find a good deal closer to the time of departure (12-6 weeks before).