Probably a problem with the charset configuration. Check the charset of the db tables and your eZ publish config on the old server and the new one. They should match.
The encoding problems are not only database related. When you move a database, you are most likely to dump into a text file, whose encoding can get damaged easily. It's best if you control that at all stages with a good text editor (under no condition MS Notepad...). Also, manage your data using proper encoding (phpmyadmin for example, for data manipulation). Things were very nasty before and after MySQL 4.1, where UTF-8 support was introduced. But many people still forget to check the previous encoding when changing or upgrading server. Actually, I've experienced several administrators who weren't very interested in differences between 4.0/4.1/5.0, and carefree upgraded their servers, thus destroying entire databases... ;) On one occasion I've also installed eZ at a server where 'SET NAMES utf8' statement was automatically called for all MySQL/PHP connections, which meant double declaration (or something like that...). Even though data was properly imported, multiple characters seemed damaged ;)
I have checked the SQL exported from my site that was uploaded online (with notepad++), all accents are present and it seems it has no problems at all.
At the hosting site I use phpMyAdmin and the character set is utf8_unicode_ci for teh database.
Maybe I have set a wrong character set just from the beggining: