If you’re unsure of the spelling, capitalization, or usage of a word, consult an authority. If you’re a writer for the Yahoo! front page, you’ve never been unsure of anything you write and probably never questioned this:
According to the Associated Press, consulate should be capitalized when it is preceded by the country. That’s also true of embassy. So if you follow AP style, the correct capitalization is: U.S. Consulate, French Consulate, U.S. Embassy, French Embassy.