It was the French brig of Way, Laurier. Here is the reference https://books.google.com/books?id=Kj1tED52ClEC&pg=RA1-PA278&lpg=RA1-PA278&dq=ship+sylphide+tow&source=bl&ots=20vMtYuscu&sig=IMVnxlCI7F7NXjYFbmP6vQs0u2I&hl=en&sa=X&ei=pRcxVduwFKm1sATSl4Aw&ved=0CB8Q6AEwAA#v=onepage&q=ship%20sylphide%20tow&f=false
Lloyd's register references another vessel named Sylphide, unfortunately. I believe that ship is Finish.
In case this rings a bell for anyone, the Captain's name was George Pasquier. From what I can gather, the ship went from Havre -> New York in 1837. other ports of call include Havana, and New Orleans. There were a few ports of call that rejected the boat because of immigration issues, however it did land in Vera Cruz and unloaded European settlers.
There was an international issue that occurred on this boat in Havana. General Tacon arrested the Captain of the Sylphide and the French Consul was not happy. Here is the story https://books.google.com/books?id=NmfW7R5VYIkC&pg=PA301&dq=sylphide+havana+general&hl=en&sa=X&ei=0RoxVeekFaz7sASMnoDIBg&ved=0CB4Q6AEwAA#v=onepage&q=sylphide%20havana%20general&f=false