SortedList throwing exception when adding french characters

I am adding some unique french words to a sorted list, but it doesn't seem to differentiate certain words like "bœuf" & boeuf".

private static void TestSortedList()
{

    Thread.CurrentThread.CurrentCulture = CultureInfo.CreateSpecificCulture("fr-fr");
    SortedList sortedList = new SortedList(new Comparer(CultureInfo.CurrentCulture));

    try
    {
        sortedList.Add("bœuf", "Value1");
        sortedList.Add("boeuf", "Value1");
    }
    catch(Exception ex)
    {
        Console.WriteLine(ex.ToString());
    }
}

So the following code above throws exception "System.ArgumentException: Item has already been added." Please help!