There are a few other good reasons to expand from 7-bit ASCII, but since you ask specifically about foreign languages, I want to tell you about that angle.
English has words with diacritical marks, usually loan words like naïve or café. They are rare, and usually you'll get into no trouble for omitting the diacritics. Occasionally one might stumble into a word that means something else when you omit the diacritical marks, such as exposé vs expose, but those cases are rare and usually the meaning can be inferred from the context without much difficulty.
The same is not true for most languages written on the Latin alphabet, though. Romance languages like Italian, French, Spanish and Romanian use diacritics much more than English does, and omitting the diacritics as 7-bit ASCII would impose would make text harder to read. The same is true for Germanic languages other than English, as many of those make heavy use of umlauts and special letters like the å found in Swedish. My native Finnish, too, considers ä, ö and å to be separate characters distinct from a and o, and telling them apart from each other is necessary to correctly parse words without needing to infer from context.
Therefore, when computing picked up pace among users who do not use English as their native language, it was essentially inevitable that the character sets should be expanded. The alternative would have been massive orthographic reforms in some of the most spoken languages in the world to make them conform to the limitations of the increasingly vital computers. That would not have worked out – although semi-official conventions did occasionally spring up (eg. replacing ö with oe). So in order to not get in the way, 8-bit Extended ASCII encodings usually lend support to these special characters, relieving at least some of the non-English languages.
Fast-forwarding to today, Unicode has support for a vast array of characters that extend the support well beyond Latin-based alphabets as well. This means almost everyone can type their native languages without the computer's charset limitations needing to get in the way.