Character sets involve a complex interaction between the character set MODX thinks is being used, the character set declared in the HTML header, the character set and collation used by the MySQL server and client, the character set and collation setting of the database, the character set of the specific table in the database, the character set of the specific field in the database, the character set of the actual data in the table’s fields, and how the specific browser responds to what it gets.
It’s a mess and I don’t pretend to understand it. I’m beginning to wonder if anyone does.
You can see what MODx thinks the set is by looking in the System Settings -- that should match what’s in the HTML header automatically. If you go into PhpMyAdmin (assuming that that’s available to you) you can see the internal settings in the Database. The PhpMyAdmin screen will tell you about what the it’s using as the default character set and collation. If you click on "Show MySQP System Variabls," you’ll see some more settings. Looking at the structure of your MODx database will give a listing of what each table is set to. Browsing the individual table in the DB with your data in will show you the setting for the content field.
It’s tempting to change the settings inside the DB, but it usually won’t help because it doesn’t change the actual characters stored and can make things worse.
Either UTF-8 or Latin1 (the most common settings) should show French characters correctly, but a lot of people seem to be having trouble with non-English characters. AFAIK, the character code for the French accented characters is the same in both so I’ve never understood why mismatches cause trouble.
One poster with a similar problem solved it by looking in the DB and writing down *everything* and then doing an install, selecting the "custom" radio button instead of
"update" and then filling in all those values. In that specific case, it was the "collation" that was off.
[Update: Lammikko posted while I was writing this. Definitely try that suggestion first.

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Hope this helps,
Bob