You can use a dynamic sized (auto-growing) input field. The search box's size would increase in size as needed while user is typing. Please remember that the initial size should still be sized according to the expected input. Check this for examples of how dynamic inputs behave:
Dynamic input field examples
Is the search-box a core/main functionality or not?
If the search-box is a core functionality:
You may consider designs like StackExchange, Google, and Amazon. They are
wide enough to accommodate any of the languages provided.
If the search-box is NOT a core functionality, then you may consider doing the following:
1- Design for the longest translation:
Find out the proper length of a search in your website in English, then
TRANSLATE that to the LONGEST translation of the languages provided. Design
your search-box width with consideration to that translation.
2- You may adopt the 27-char search-box width rule (I am not sure if this rule studied different languages or English only).
For websites like StackExchange, Amazon and Google. Search is a vital main functionality for these websites, hence it is placed in the middle of the main page and it is a wide search box.
Compare that to Samsung website for example, where Search is not a main functionality, it is placed on the side and has just a reasonable width.
Very useful reads:
I am providing several resources that I found very useful, not just to help you design a Search-box for different languages/cultures, but also help you UX design the whole website for different languages/cultures.*
- This article Design a Perfect Search Box highlights the importance of having a proper size search-box:
Making the input field too short is a common mistake among
designers. Of course users can still type long queries in a short
field, but only a portion of the text will be visible at a time and
this equates to bad usability, since users cannot review and or edit
their full query. In fact, when a search box has a limited number of
visible characters, users tend to use short, imprecise queries, since
longer queries become inconvenient to read. If input fields are sized
according to their expected input they are both easier to read and to
interpret for users.
- This article 3 things to keep in mind when designing UI to be translated in different languages discusses how the same message takes different amount of space in different languages and how this difference in the amount of words and characters needed to convey the same message can ruin an interface or make it unusable. See images below:
English vs Ukrainian
The word "Views" translation ratio:
Design a Perfect Search Box
Best Practice for designing UI for a multilingual site?
Design considerations for internationalization
3 things to keep in mind when designing UI to be translated in different languages
UX Design Across Different Cultures — Part 1
UX Design Across Different Cultures — Part 2
Is there a recommended size for search boxes?