You can restore your database using this command
mysql -u someuser -p --default-character-set=utf8 somedatabase < backup.sql
This overrides the default client character set.
I would also make sure that my tables are also in utf8.
So when you open up your backup file with a text editor, you should see utf8 as the DEFAULT CHARSET
CREATE TABLE `sometable` (
`c1` varchar(10) NOT NULL
) ENGINE=InnoDB DEFAULT CHARSET=utf8
If you are still having problems, check your backup and make sure that the actual data being restored is correctly formatted. If you had a character like é for example, it should show up as é when you view it in a text editor and not as é or some unreadable symbol.
One additional note. utf8_general_ci and latin1_swedish_ci are collations and not character sets. Character sets like UTF8 can have multiple collations, some are case sensitive _cs and others are case insensitive _ci. Collations set rules for character comparison and sorting.
http://en.wikipedia.org/wiki/Collation