Different aspect on different browsers I'm using Drupal 7, Webform module, and Bootstrap Sub-Theme.

I'm facing a browser problem and an admin/end-user problem.

As a French speaker I would like to have my error messages in French.

In Safari (as admin), it shows errors in red box as in this example:



This is my result in Chrome (as admin):



And this is my result in Firefox (as anonymous):



Chrome (as admin) is working with translation automatically (as shown in the example above), but not Firefox (as end-user).

Safari and Chrome (as admin) use a different way to display errors.
Safari got red box for every errors.

Chrome uses a red box just for web form validation (module) errors.

I would like to have errors in French and in red box for end-user as well.

End-user have to answer a Captcha.

Any suggestions to resolve these issues?
Even though you didn't mention it, this is clearly a multilingual site. Which implies that "language detection" is involved (to decide each time in which language a page (or webform) needs to be displayed.

Your problem related to the usage of French or English language might be because of the "language detection" configuration. 

So check this configuration via Configuration -> Languages -> detection and selection: experiment a bit with the correct order that should be used. Often times, this should be changed to something like 'URL, Default, User', and not something like 'Default, URL, User' (which I assume you're currently using, and which might explain the difference in the language used in different browsers).

The browser differences to display the errors (red boxes, etc) might be some browser dependency and/or something in your sub-theme (custom or not?). With the few details provided it is hard to tell what might help to resolve that part of your question. I recommend you move that part to a different (new) question, or enhance your question to provide more details about the sub-theme.