[Generally I really suggest to do a test run with an example album to be sure how it works on your server befoer starting such large projects. We can't know about all possible configurations.]
Excellent advice and, in fact, what I am doing. Debugging the transmission of data (making sure character sets are preserved at every step) is a separate problem from being sure that once correct data gets into the Zenphoto database, it will be displayed correctly. From your responses and my testing, it looks like French will be displayed properly.
So, any problem I have with preserving French characters during uploading of data is elsewhere than in Zenphoto. And I confess I don't know whether DreamHost includes mbstring in its standard configuration of PHP; I'll investigate. As you point out, it's a necessary condition of using the utf8 character set successfully.
Thanks for your attention to my questions,
Harvey