My first question is why did you send a friend request to a complete stranger on Facebook?
Is Jeanne male or female? You said "he asked the following question" so I assume Jeanne is male. If you are male, then be aware that saying "your good looks prompted me to befriend you" will make many people assume that you are romantically interested in Jeanne.
If you're happy with that then I would say "Hi Jeanne. Sorry I didn't get back to you sooner. I decided to send you a friend request because your profile suggests you are intelligent and good-looking".
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