Bruce's idea is a good one, but really, the possible combinations you could create from your list are numerous:
Berlin has magnificent museums (art, archaeological, historical) and a wealth of historic sites, especially from the WW II and Cold War periods. Although I wouldn't care for the weather in March, I can well understand that you would not fear it. And I'd say it's a more indoor-oriented city than many on your list. It's also comparatively inexpensive--though I don't see a problem with your budget in any case.
Nice and the south of France: I just don't know. March is well and truly "off season" there. Nice is a big, functioning city so definitely would not be dead. Menton is warm enough that it has a lemon festival in mid-winter (I think in February), and I liked the two large gardens there. Still, I'd want input from people who've done the Riviera in March. I was surprised at how much cloudy weather I had in the area around Nice in the first half of May this year, thought the temperature was pleasant if not especially warm. A lot of the attractions have more limited hours and/or days of operation in May than in mid-summer, and probably more limited still in March. You could work around those limitations; I'm thinking more about what that means about the general atmosphere, if tourism is down so much that a museum is only open four days a week, rather than six or seven.
Be especially careful if you're thinking about Provence. The mistral (wind from the north) makes for really miserable conditions when it chooses to blow.
Check Amsterdam's weather data carefully. Several people I met in Europe independently mentioned that it can be really depressing, chilly and damp. Wikipedia's weather-summary chart suggests that a dearth of sunlight may be a significant factor. March has just 126 hours of sunlight, on average. Obviously, that situation improves as you move toward the end of the month. On the plus side, tulip season begins around mid-March (though it's weather-dependent), so if you have an interest in the flowers, this would be a great opportunity to see them.
Barcelona is one of my favorite places, with fabulous modernista architecture as well as a large historic area, plus very good museums. There's lots to do there, and the weather is comparatively mild. There's fast train service between Barcelona and Paris, so that would be a workable combination.
I don't think March is a very good time for the Italian lakes.
I really liked Montenegro when I visited it in 2015. It's got a lot of attractive towns, some with a Turkish vibe, and some very pretty countryside. But it feels more like a wander-around-outdoors sort of place to me. The weather might be OK; take a look at what wunderground.com has for historical weather stats. (The site isn't working for me at the moment. You'd need to enter a city --I'd use Kotor, then choose Historical, then Monthly, then use the pull-down box to select March.) But I think it could feel sort of abandoned out-of-season. They were practically rolling up the sidewalks in Budva on the day I was there in early October 2015. I think for a honeymoon you'll want the occasional festive evening (a lively restaurant, at least), and I'm just not sure that Montenegro runs to "festive" in March. The easiest place to combine with Montenegro would be Dubrovnik, but you've already been there.
