Brief History: Until the French Revolution of 1793, Coutances was the capital of the the region of the Cotentin. What was chosen from the town was (and it seemed quite an obvious choice to me from the photos I've seen) the Notre-Dame Cathedral with two classic front towers and an unusually high (66 meters, from what I've read) lantern tower in the back - you can see it in the pic of the miniature, by the way. Started in years 1040s by the local bishop Geoffroi de Montbray, the cathedral was later paid for by the de Hautevilles from the money they gained in Sicily where they've founded a kingdom.
Why I think it was chosen: I must admit I thought really hard to find possible reasons. The best ones I could come up with were the Cathedral's really unusual tower, coupled with the fact that it looks like it's one of the prime Normandy sights.
What I'd choose: If I am to believe pictures and books, Coutances would indeed by in my miniature list for Normandy, together with Mont St. Michel and Rouen.
Brief History: The first of the monument I mention that I've actually seen not only in miniature - a welcome change. Arc de Triomphe suggests one of those ancient Roman arches, only it's larger. Actually, it's the biggest triumphal arch in the world, about 49m high and 44m wide. Divide it by 30 and you'll get the sense of what the size of the miniature in the park actually is. Commissioned by Napoleon in 1806 to commemorate the victories of his Grand Armee, It wasn't completed until 1836, under the reign of Louis-Philippe. Four years later, Napoleon's remains, brought from St. Helena, passed under the arch on their journey to his tomb at the Hotel des Invalides. Since that time it has become the focal point for state funerals. It's also the site of the tomb of the Unknown Soldier, in whose honor an eternal flame is kept burning. Though you won't see the eternal flame in the park.
Why I think it was chosen: Because it is one of the landmarks of Paris - no shade of doubt about that in my mind.
What I'd choose: I'd definitely include Arc de Triomphe with other Paris monument, though I'd probably would have included a couple of Parisian parks and gardens.
Brief History: Azay-le-Rideau is probably one of the few cases of beneficial corruption, for the castle was built by Philippa Lesbahy, wife of Francois I's corrupt finance minister. I guess some of the money went to pay for this masterpiece. And another one of my travel goals for France. Balzac called Azay-le-Rideau 'A multi-faceted diamond set in the Indre'.
Why I think it was chosen: The castle of Azay-le-Rideau presents a really fairytale-like picture, a Gothic castle set on the river and with many attractive moats. Tourist interest should have proved an additional persuasive argument.
What I'd choose: For the village of Azay, the castle. I'd probably put it on display for the region of Loire along with Cnambord, Chenonceau, Usse, and some others. So, with respect to Azay-le-Rideau, I feel like agreeing. Besides, it looks like a pretty toy on actual photos, so it seems to have been made for the park!