Charset meta tags should not be necessary. HTML5 doesn’t support them at all, and UTF-8 should be the default. Most likely, the characters being shown on the page are simply not valid UTF-8 characters to begin with.
Is the text that’s not rendered correctly being loaded from the database? If so, please check if the characters are being displayed properly in phpMyAdmin, and that your PHP code sets the right database connection charset. I just wrote something about that for someone else here:
If the text is not from a database, please make sure that the file is saved with UTF-8 encoding too. Notably Windows Notepad has the tendency to save files with Windows specific encoding that doesn’t work on anything that’s not a Windows computer, including websites. One quick way to verify this is to try to open a file with our File Manager. If it cannot open the file, it means the file is not valid UTF-8.