The browser itself doesn't have an encoding. It supports many encodings and uses the one you tell it too. If you specify (in headers and/or HTML) that the encoding is ISO-8859-1, then your document should be in that encoding and you should make sure that all characters you send are in the right encoding. So you should actually send ISO-8859-1 characters. You cannot send a document that uses different encodings for different sections of the document.
For some characters, you may post an HTML entity instead. For instance é can be sent as é. This will work, regardless of encoding.
If you have the choice, I'd opt to use UTF-8. It supports any character and you don't have to worry about escaping diacritics or other special characters, except those that are special to HTML/XML itself.