There are three ways to manage multi-languages:
Different events, categories, menu links, etc by language
It's the usual Joomla! way. The disadvantage is that you different events with separate registrations, etc. All is separate without any issue.
Use the provided tags in the backend to manage the title and the description for any event.
Use language Joomla overrides for the title, etc.
For example, define the title of the event in COM_ALLEVENTS_MON_EVENEMENT_TITLE, then create the language Joomla override. For additional information about the language overrides, goto the Wording Modification (Language overrides).