Be careful about Croatia. It could end up in the Schengen area before your trip.
I am currently on my sixth recent trip of three months or longer, but all have been post-retirement, so I'm not sure what rhythm would be practical for you. My usual reaction to plans to stay in one place for a month or longer and "see Country X" is that--assuming we're not talking about a very small country--it's not practical because of the limited reach you'd have from any single base. In much of western Europe the express trains will help a lot, because you can travel great distances within 2 or 3 hours, but ticket costs for those trains will be really painful if you want to remain flexible (responding to weather conditions, demands of work, etc.) and buy the tickets only a day or two ahead.
And then there's the issue of paying for lodgings in two places for the same nights. I remain unconvinced about the financial practicality of that approach if you want to do a lot of traveling away from your base. Much depends, I think, on what sort of places you plan to side trip to, and whether you can motivate yourselves to get up super-early for a 7:30 AM train so you'll have a long day at your destination. The thing is, many of the top not-London, not-Paris destinations have way more than one day's worth of sights. It would be expensive and annoying to keep making day-trips to the same place, and decamping for three nights to a destination like York would be very costly from a lodging perspective. What I'm saying is that I'm not a fan of day-tripping to York from London or to Strasbourg, Colmar or Bordeaux from Paris.
But as I said, needing to work during the trip makes a big difference.
I like the way James has mixed things up, but in London and Paris I think I could spend a month with just a modest number of not-distant out-of town trips to smal towns worth just about a day but not requiring re-visits. I think two weeks in those two cities would be too short with a bunch of day trips or weekends away.
If the trip must be in June-August, that does limit the places I'd recommend staying for an extended period. Planning five nights in Paris in July is risky, but it's only five nights. Renting a place in Paris for the month of June, July or August is something I simply would not do. But Normandy and Brittany would be fine destinations at that time of year. You might get a few days of spiking temperatures, but not an extended, miserable heatwave. Unfortunately, you cannot see even one of those areas from a single base, so you'd need to pull up stakes and relocate a lot more often than you'd probably prefer. Similarly, any place at altitude will be mostly not-hot in the summer, but such places aren't convenient bases for a bunch of side-trips unless you primarily want to go on hiking excursions.
If you haven't been to the stretch of Spain between the Basque Country and Galicia in northern Spain, that's also a great area for a summer visit. But again, fairly short stays in multiple bases would be needed to fill more than a two-week segment of your trip.
The Scandinavian capitals could work, but lodgings are quite costly, and so are restaurant meals in Norway. Trains aren't particularly cheap; nor are the buses in Norway. Tallinn, Riga, Vilnius and Gdansk are meteorologicalyl suitable and much less expensive. I don't know how long one could stay in any of those places, taking an occasional day trip, without getting antsy. I'd guess at least two weeks in Copenhagen and Stockholm, probably somewhat less in the others--though I just did nine nights in Oslo with no out-of-town trips and no local hikes, which are easily managed via local transportation.
I'd also look at Poland beyond Gdansk, but it's a large country that sort of requires stays in a bunch of different cities. I really enjoyed Warsaw, a real-world city with many historic sights though not a huge amount of historic architecture.
