Firstly just to clarify: the name means "City of Architecture and Heritage". We visited it for two reasons: I'm interested in architecture, and it was conveniently situated for lunch opposite the Eiffel Tower (which we had visited in the morning). As an added bonus, we had a Paris museum pass which included entry to this museum.
All I can say is WOW! The museum seems to be little known with hardly anyone there, especially not foreigners. But it is full of exhibits which could save you a lot of traveling around: most of the most amazing buildings in France are presented in one place.
The ground floor has plaster casts of spectacular building facades and statues, mainly from churches. This may not sound all that amazing but some of the casts date back to the 19th century and are life-sized and detailed. They reminded me of some of the larger exhibits in the British Museum, but there are far more of them. And they record some interesting historical events for example there is a set of statues of saints with their heads removed. Apparently this decapitation took place during the French Revolution as part of the backlash against the established church. The "originals" have been restored but the plaster casts have been left headless, just as they were when the casts were taken.
The upper floors contain more recent architectural examples with smaller models but interesting information about the way in which they were designed. There is even an entire walk-in replica of an apartment from Le Corbusier's Cité Radieuse in Marseille.
At one end of the upper storeys is what feels like a separate museum in itself, a maze of rooms decorated with full-scale copies of medieval and Renaissance murals. They seemed to have filled every space with rooms carefully crafted to be exactly the right size for another mural. Keep your eyes open for almost-hidden entries and corridors; if you walk along these you may well find yourself in another series of rooms which you didn't realise existed.
Almost all of the labels are in French, but keep your eye out for periodic information cards which tell you about the highlights and are available in several languages. Because it covers a range of periods it will suit those with both classical and contemporary taste, and the few children we saw seemed to enjoy it as much as the adults (there are a few hands-on activities dotted around especially for the youngsters).
In terms of accessibility, the main halls are fully accessible with a lift between them. I'm not so sure about the mural area, there are a lot of short flights of stairs and I did not see any lifts or stairlifts.
And the cafe – which is also accessible – had a range of hot and cold food and great views of the Eiffel Tower at a very reasonable price.
All in all however a highly recommended visit!