I'd love some help from folks who know Paris (and the area around) well. My girlfriend and I will be traveling to Paris at Christmas, and I'm looking for a place to propose.

Something classy and romantic but non-traditional or touristy (she's been going to Paris on vacation for ages, I've been a few times), ie, she'd say no if I chose the Eiffel Tower, etc. I'm a more private person, so I think that I'd prefer something quieter or less crowded (ie, I don't think I want to do it at dinner in an expensive restaurant, etc.). I was thinking of planning the entire day as something interesting and memorable, and then proposing late afternoon/evening ish. And I'm willing to pay for access for something unforgettable (private access to a museum or chateau or whatever), but she's not the type impressed by cost/expense alone. We're art/food/architecture/music/opera type folks, but I'm just looking for options, preferably options that would make for a story that we will still tell fondly 20 years from now.

And I'm certainly not limited to Paris--but I'd like to do it all in one day. I'm happy to wake up early and venture by train/plane/car some place extra special for the day.

Apologies if this is nebulous, but I'm still planning it out mentally--but advice and counsel from those who have been there (literally and metaphorically) would be appreciated. Thanks!