There’s no definitive answer to that.
Some people feel it was because Sarkozy wanted the commemoration to be a strictly American-French affair, for his own political domestic purposes. No members of the British establishment were invited until they started agitating for an invitation, and the French then started inviting only those who they were pressured to do so - initially Prime Minister Gordon Brown and only at the last minute inviting the Queen and the Royal Family.
Other people feel it was incompetence on the part of either the British government or the French or both in simply not following the correct procedures surrounding such an invitation.
Still others think it was a deliberate snub.
Some have also suggested the White House might not have wanted the British royals there.