The OP's complaint is valid. In a game undeniably based around communication, a language barrier is a formidable one. Cries of "that's racist!" are sure to emerge, and indeed already have, but these are red herrings. The language barrier is most prevalent in pre-game chat, where there are no pings or other universal markers that transcend languages. I speak spanish fluently, so I am in a better position than many, and still I find it highly frustrating when somebody like a Brazilian comes on and speaks Portuguese or a Quebecer comes on and speaks French. Do they deserve to play the game? Of course. Do they deserve a pleasant gaming experience? Of course. But so do I, and my gaming experience is thoroughly ruined by a player or players that cannot or will not communicate with me. Sure, it may be seen as more benign if they simply don't speak my language, but loss of league points, time, and energy is just as frustrating to be lost by somebody who doesn't speak my language as to be lost by a troll.
My suggestion is this: Add a plugin, or other add-on, to the pre-game champ select screen. Have common phrases in that plugin and, when the button next to the phrase is pressed, the phrase is broadcast in all languages league supports in the chat.
Example: (press button that says "Hi")
Shifty:98 Hello Hola Bonjour etc
Examples of things to include are things such as "I'd like to play top/mid/etc" or "Please don't ban/ban champ X/Y"
I'm sure i'm missing a few things, that other posters will contribute.
Simply remember that this IS a problem, and that shouting RACIST! at the OP won't solve the problem, and is a red herring argument.