Yes. The currency on the French side (St. Martin) is the Euro, although the U.S. dollar is widely accepted. In Dutch St. Maarten, the currency is the Netherlands Antilles Florin, which exchanges at a fluctuating rate.
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Both are the same island, despite the two different spellings. The difference really only refers to location. French is the official language of St. Martin and Dutch is the official language of St. Maarten. However, English is widely spoken on both sides of the island. Driving from one side to the other is generally quick and easy.
Most of the hotels and resorts on the island are closed during September and October and re-open for the Holidays.