A quick way to find out is simply to perform a web search on the term. Most of the first hits will be to articles or web pages that use the customary capitalization.
The first it on a search for "eiffel tower" is the "The OFFICIAL Eiffel Tower website: tickets, news, info..."
The first hit on a search for "arab countries" is from a description of the League of Arab States, and it shows: "Currently it gathers 22 Arab countries: Algeria, Bahrain, Comoros, Djibouti, Egypt, Iraq, Jordan, Kuwait, Lebanon, Libya, Mauritania, Morocco, Oman, Palestine, Qatar, Saudi Arabia, Somalia, Sudan, Syria*, Tunisia, the United Arab Emirates, and Yemen."