This is a bit hit & miss, however try
[email protected]
or try calling - 06 90 569104. UK mobiles do not seem to work on local numbers when you get there.
They had 3 a/c once upon a time prior to a hurricane.
I managed a flight in the one remaining PA-28 in Nov '09. It was an N reg, old but it flew okay, but last year could not get a reply and did not bother driving to Grand Case.
They have a small club facility to the east of the small terminal however I think is only manned by members as and when they go flying.
There is a chap there whose brother lives on St. Barth's and he may offer to take you along if they still have a serviceable plane. I may still have his e-mail address, but he did not reply last November.
If you manage to contact anyone please let me know as I shall be back there soon.
This may be a bit hit and miss however well worth the effort to make it happen.