Datbase Content Type - Cleaning Up Existing Content

Hi everyone,
After a database update on our custom built CMS a few months ago it seems to have adjusted the content type to show apostrophes (') to look like this: ’
It also gives similar looking characters for double quotes and special characters like these ones: à

Does anybody know what the content type should be set as in order to display these characters properly? I am hearing “UTF-8” but not sure if that’s going to fix this or not? Are we stuck with these characters in the database or is there a way around it? These characters were copy and pasted from the internet when the content was originally added. When new content with apostrophes are added in they will work fine now but for all existing content they still have those buggered looking characters.

Any help for cleaning up this existing content is greatly appreciated. Should we be looking in the database directly?