Accent caracter encoding
The contents of your tables are not stored in the encoding that is specified for those columns. So you need to find out how the characters are stored and what the specified encoding is, e.g. using phpMyAdmin. It seems the characters are stored in UTF-8, but the columns are identified as latin1. If I recall correctly I've used this conversion script successfully in the past for a similar situation. Of course, always backup your database before attempting such operations! Or try it on a copy first.

You can also drop all tables and fully reimport the old database, this time choosing the correct character encoding. (It's best to have everything in UTF-8, so if the old database dump is not in UTF-8, you could convert the .sql file first and then import it as UTF-8).