no, looks ugly. "the Eiffel Tower" looks better.

Unless the article is specifically part of the name, it is not capitalized. For example, the American store, The Home Depot, has a capital 'T', because that's the name of the store (though commonly referred to just as Home Depot). However, if there is only one of a particular store in your town, but the 'the' is not part of the name, it is not capitalized. ie Let's go to the Walmart. There is only 1 (real) Eiffel Tower, so it needs the definite article. But since it's not part of the name, it is not capitalized = the Eiffel Tower.

Nice question!

Yes Martin is right. I’m sorry that in my correction I wrote The. It’s not incorrect that way but it’s better written ‘the Tour Eiffel’