multiple language website navigation menu suggestion

Should the user create multiple menus for each language and load the relevant menu?

Yes

Obviously menus are part of the content of the site, and no one else except for the site owner can decide what will be the content.

I find this difficult to handle for the user. Is there any other way of changing the language of the menu?

Sure, localization is hard. You can use the google translate API to translate automatically. IMO this approach is not recommended to any site that don’t want to be ridiculed (google translate is good enough to give a general meaning of phrases, but from time to time it will give you a funny translation that is out of context).

side note: you are reinventing the wheel. This kind of localizations is usually solved by using dedicated plugins like WPML or by setting different sites (maybe over a network installation) per each language.