Crossword Compiler can be used in many languages, and supports the full unicode character set (with some minor restrictions).
Each Crossword Compiler word list has an associated character set, which can either by Unicode if it supports all characters, or a specific reduced character set (e.g. Western, Greek or Cyrillic). In most cases it makes little difference which you use. Using Unicode has the advantage of supporting anything in any language. Using a reduced set may be helpful if you want to avoid words containing words in foreign character sets (e.g. when importing text word lists from multi-language sources).
You can change the character set associated with a word list in the Word List Manager. Select the word list that you want to change, and then select Character Set... from the Word List menu. Then click on the set that you want to use. If you check the Save as default box each new word list that you create will automatically use the character set that you have selected.
Although the program supports the full Unicode character set, there are some restrictions: the Grid Filler can only use 63 distinct characters at a time, which in practice means that for example you cannot use Chinese words to fill a grid (there is however no problem using Chinese for clues or individual squares). It also only supports single-entity Unicode characters, not extended characters made from extended combinations of individual characters.