A plane owned by James Horner -- the Academy Award-winning composer of "My Heart Will Go On" -- crashed Monday morning, killing the pilot. Law enforcement sources tell TMZ ... the 2-seater S312 Tucano MK1 -- a single-engine turboprop -- went down at 9:30 AM west of Santa Barbara. We're told the pilot was alone in the aircraft when it crashed, but authorities have not identified the body. Horner composed soundtracks for Hollywood's top directors – Stephen Spielberg, George Lucas, Ron Howard, Mel Gibson -- and won an Oscar and a Golden Globe for "Titanic" ... which included Celine Dion's massive hit. 61-year-old Horner is a known recreational pilot ... much like Harrison Ford.