The New Orleans-born Blanchard developed a love for music early and began studying piano at the age of five. He later switched to the trumpet and subsequently enrolled at the New Orleans Center for the Creative Arts (NOCCA), where he studied with Ellis Marsalis and George Jenson. While at Rutgers, Blanchard continued his music studies with Kenny Barron, Paul Jeffries and Bill Fielder. During his sophomore year, he was invited to join Lionel Hampton's orchestra and he left school to tour for nearly two years. In 1982, Blanchard and saxophone player Donald Harrison were selected to replace Wynton and Branford Marsalis by Art Blakey for his Jazz Messengers. Blanchard began composing and his work was included not only on Blakey's "New York Scene" album but also on two albums recorded with Harrison. After four years with Blakey, Blanchard and Harrison left to form their own jazz quintet.

Film director Spike Lee tapped Blanchard and Harrison to play with the Natural Spiritual Orchestra on the soundtrack for "School Daze" (1988). The pair were invited by Bill Lee to perform on the soundtrack to "Do the Right Thing" (1989). Around this time, however, Blanchard began experiencing problems. In his own words, "I thought I was using too much pressure when I played. Later I found that my problem was in my embouchure . . . since childhood, I had been playing incorrectly with my bottom lip over my bottom teeth, which often caused me to cut my lip." Recognizing that he needed to correct the problem in order to further grow as a performer, the trumpet player severed his partnership with Harrison and began to re-learn how to play the trumpet.

When Spike Lee approached Blanchard about working on his next film about a jazz musician (1990's "Mo' Better Blues"), the musician was prepared. He had formed a new quintet and was under new management. Agreeing to work with Lee, Blanchard served as technical advisor, coaching Denzel Washington and dubbing Washington's trumpet playing. Lee had liked one of the themes the musician had created and invited Blanchard to try his hand at composing the score for "Jungle Fever" (1991). The jazz-inflected score was the first of several collaborations between Lee and Blanchard. Many critics took note of the composer's lush, beautifully orchestrated score for Lee's "Malcolm X" (1992). Capturing the tenor of the film's four-decade span, the music encapsulated the pleasures as well as the pain of the African-American experience providing an emotional context for the film's events. (Blanchard, who appeared in the film as a trumpet player, recorded a variation of the score, "The Malcolm X Jazz Suite", which also earned widespread acclaim.) He subsequently provided the appropriate music for Lee's "Crooklyn" (1994), "Clockers" (1995) and "Get on the Bus" (1996). In addition to his work with Lee, Blanchard has also provided the jazz scores for "Sugar Hill" and Matty Rich's "The Inkwell" (both 1994), and contributed music to "'Til There Was You" (1997).