Accented characters to Firefox: how?

[djc]

I'm sure the answer to this must be something simple about encodings, but I 
haven't figured it out yet.  Can you help?

Under Windows I edit text in emacs 22.3.1 with Western European accented 
characters like ä, ü, ç and Ê, and I want to copy it from emacs to a 
Firefox mail composition window.  But the text appears correct only up to 
(but not including) the first accented character, and after that is either 
a series of question marks or else is strangely formatted including 
question marks.  For instance, the text

    ...accented characters like ä, ü, ç and Ê, and...

from the Emacs buffer becomes

    ...accented characters like ??, ?????, and...

How can I make this work properly?

Thanks.

Pete