There are 2 ways clients can access the booking widget: 1) from your booxi booking page, and 2) from your website (in case you added a book now button there).
Widget accessed from your booxi booking page: the language is determined by the default language for your business (My Business tab > Booking rules). The client can change the language if he wants (see here for the list of supported languages).
Widget accessed on your website: the language is determined by the language value configured in your button code.
To set the language, add the corresponding 3-letter identifier for the target language as shown below (example for Swedish).
To find the language's identifier, select a language in the code generator.