Will the car fit? Yes. Can you fit some tools? Yes but it won't give you a lot of room.
Can you tow it with that truck? What's the GCWR?
Edit: page 21 https://www.fleet.ford.com/resources/fo ... 03_All.pdf
GCWR is 12.5 or 13k. Truck is probably in the 7500 pound range. So your towing capacity is 5-5500. Your car weighs approx 3000...that means the trailer can't be more than 2-2500. That's with NOTHING but the truck, trailer, car...nothing additional in the trailer OR the truck. No clothes, no gas, no tools, no crew, nothing.
I doubt that an 03 F150 weighs that much. My 2008 F250 SuperCab diesel weighs 7200lbs with 1/2 tank. The 150 should be quite a bit less.
I agree with gobuffs assessment on the car fitting in the trailer. It will fit, but little room for other stuff. With a 1998 F150 5.4 4wd extended cab, I used to pull a Mustang Cobra (3200lbs) in an 18' enclosed. Little room for anything else, but it fit. Similar size as a 330. The truck will do it, but be patient when pulling out in traffic and give yourself PLENTY of room to brake. Also, be very aware of your load leveling and where the car is sitting in the trailer.