Air France offers a weekly one-day special. Today it is St. Martin. Christmas seems to be excluded, but I saw the cheap fare in December and January. Don't know how long after that. Price is Chf 799 (exchange rate is about 1:1).

The Paris-SXM-EIS route is the best one I know to get from Europe to the BVI quickly (one day) - and no Liat.

http://www.airfrance.ch/CH/en/local/resainfovol/meilleuresoffres/wow_page.htm