Well, “Lett,” as suranyi notes, is also used in English, and checking the dictionary, it appears the derivation of that is from the German leute, meaning “people.” So my guess is that “Lettonie” means something like “place of the Letts” or “Lett-land” or something to that effect.
A very long list can be found on Wikipedia. Look in the left sidebar below “Languages”. When you hover over a link to Latvia’s page in the respective language wiki, the page name appears in your status bar.
Good tip! It looks like it’s about 50/50 for Latvia vs. Lettonie derivations. Now to try and figure out who these mysterious Letts are. Wikipedia talks about Curonians, Latgalians, Selonians, Semigallians and Livonians. Maybe there never were any Lettish people per se. They were just all called people (leute) by the Germans and the name stuck.
“Latvians occasionally refer to themselves by the ancient name of “Latvji,” which may have originated from a “Latve” river that presumably flowed through what is now eastern Latvia. A small Finno-Ugric tribe known as the Livs settled among the Latvians and modulated the name to “Latvis,” meaning “forest-clearers,” which is how medieval German settlers also referred to these peoples. The German colonizers changed this name to “Lette” and called their initially small colony “Livland.” The Latin form, “Livonia,” gradually referred to the whole of modern-day Latvia as well as southern Estonia, which had fallen under German dominion.”
Rule of thumb: whenever the French and English names for something differ, the majority of Romance languages will be similar to the French version (Spanish and Romanian seem to be the ones with the highest probability of having a word from a completely different origin).
These are regions of Latvia, by and large. Courland is the peninsula separating the Gulf of Riga from the Baltic; Latgale is the rural southeast, adjoining the Lithuania/Belarus border area; Livonia is a territory in the northeast and southern Estonia, originally inhabited by the Livs, who spoke a Finnic language akin to Estonian (only a few hundred speakers left today). Selonia was west of Latgale, and Semigallia west of that, occupying most of the Lithuanian border area, abutting on Courland. Samogitia is the far southwest, being principally a (northwetern) region of Lithuania that overlaps the Lithuanian/Latvian border by a bit.