Franklin played on Hugh Masekela's 1968 number one single, "Grazing in the Grass," as well as with Masekela's band at the Monterey International Pop Festival in June 1967. In addition, Franklin has played and recorded with Gene Harris & the Three Sounds, Hampton Hawes, Freddie Hubbard, Bobbi Humphrey, Willie Bobo, Archie Shepp, O.C. Smith, Count Basie, Stevie Wonder and Al Jarreau. Franklin's recording—composed by Sanifu Al Hall, Jr.-- "Soft Spirit" was featured on the breakbeat compilation Tribe Vibes as it had been sampled by the musical group A Tribe Called Quest.
While attending the Manual Arts High School he played with his first professional band – the Roy Ayers Latin Jazz Quintet. Around that time, Franklin worked with Harold Land and Hampton Hawes. Years later he would tour Europe with Hawes and record five albums with him. In Los Angeles, Franklin also played with Ornette Coleman, Don Cherry, Billy Higgins and Scott LaFaro.
In 1968, after a year-long tour of the East Coast playing with Willie Bobo and working gigs on his days off with Archie Shepp, Lamont Johnson, Beaver Harris and Roswell Rudd, Hugh Masekela heard Henry play and made him an offer. Three and a half years later the two would collaborate on Grazing in the Grass.
He continued touring over the next few years, working internationally with singer O.C. Smith, The Three Sounds, Freddie Hubbard and Count Basie. Franklin collected another gold record with Stevie Wonder on Journey Through The Secret Life of Plants.
Working with John Carter and Bobby Bradford, he produced two albums: Self-Determination Music and Secrets.
With Dennis Gonzales, John Purcell and William Richardson he performed on five albums played extensively with Pharoah Sanders, Joe Williams, Sonny Rollins, Bobby Hutcherson, Sonny Fortune and Milt Jackson.
Franklin appears on more than 100 albums, with many of them produced under his leadership, and has also published a method book for all bass players entitled, Bassically Yours.
With Dennis González
With Hampton Hawes
With Bobbi Humphrey
With Hugh Masekela
With Julian Priester
With Freddie Redd
With Woody Shaw
With The Three Sounds