MySQL matching unicode characters with ascii version

I'm running MySQL 5.1.50 and have a table that looks like this:

organizations | CREATE TABLE `organizations` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `name` text CHARACTER SET utf8 COLLATE utf8_unicode_ci NOT NULL,
  `url` text CHARACTER SET utf8 COLLATE utf8_unicode_ci DEFAULT NULL,
  `phone` varchar(20) CHARACTER SET utf8 COLLATE utf8_unicode_ci DEFAULT NULL,
  `timestamp` timestamp NOT NULL DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP,
  PRIMARY KEY (`id`),
  KEY `id` (`id`)
) ENGINE=MyISAM AUTO_INCREMENT=25837 DEFAULT CHARSET=utf8 |

The problem I'm having is that MySQL is matching unicode characters with ascii versions. For example when I search for a word with that contains an 'é', it will match the same word that has an 'e' instead, and vice versa:

mysql> SET NAMES utf8;
Query OK, 0 rows affected (0.00 sec)

mysql> SELECT id, name FROM `organizations` WHERE `name` = 'Universite de Montreal';
    +-------+-------------------------+
| id    | name                    |
+-------+-------------------------+
| 16973 | Université de Montreal  |
+-------+-------------------------+
1 row in set (0.01 sec)

I get these results both from PHP and the command line console. How can I get accurate matches from my SELECT queries?

Thanks!