Pierre Dewey LaFontaine Jr. was born in New Orleans on July 3, 1930, the son of Pierre LaFontaine Sr., a truck driver and part-time musician who later shortened the family name to Fountain, and his wife Madeline. He was a sickly child with weak lungs, and a neighborhood doctor suggested that his father buy him an instrument he had to blow into; he chose the clarinet. He took private lessons but learned jazz mostly by playing along with records, first by Benny Goodman and then by the New Orleans clarinetist Irving Fazola. By his teens he was working regular nightclub gigs on Bourbon Street, and by his own account he was earning union scale, about $125 a week, while still a high school senior. The Guardian's obituary dates his first band, the Junior Dixieland Band, to 1948, and his recording debut to 1949, when he joined the drummer Phil Zito's band; he also worked early on with the bandleader Monk Hazel.

In 1950 he co-founded the Basin Street Six with his friend, the trumpeter George Girard, and in the mid-1950s he led his own group, billed as Pete Fountain and His Three Coins, which made the Southland label album New Orleans to Los Angeles (1956). He spent several months in Chicago with the Dukes of Dixieland, then returned to New Orleans to play with bands led by the trumpeters Tony Almerico, Sharkey Bonano and Al Hirt, his friend since their teens. Fountain and Hirt led a band together through an extended residence at Dan Levy's Pier 600 on Bourbon Street, and the two were often paired in public as the faces of New Orleans Dixieland.

His national break came through television. A talent scout who saw him at the Pier 600 brought him to the attention of Larry Welk, the jazz-loving son of the bandleader Lawrence Welk, and the elder Welk hired him for his orchestra in Los Angeles. For about two years from 1957 Fountain was featured every week on The Lawrence Welk Show with a small Dixieland combo, which made him a household name. He left in early 1959. The common story is that Welk refused to let him jazz up a Christmas carol on the 1958 Christmas show; Fountain's own autobiography says he did play a jazzy "Silver Bells" and that it displeased Welk. His public explanation was that "champagne and bourbon don't mix."

The Welk exposure led Decca's A&R chief Charles "Bud" Dant to sign him to Decca's Coral label, where Dant produced dozens of Fountain albums; the Guardian counts 43 on Coral. His recording of "Just a Closer Walk with Thee" became his signature piece, reached number 93 on the Billboard Hot 100 in 1960, and by the Guardian's account sold half a million copies. In October 1959 his hometown held a Pete Fountain Day, and a concert at the Municipal Auditorium that month was recorded for an album. His regular quintet, which he called the Pete Fountain Quintett, centered on the drummer Jack Sperling, the vibraphonist Godfrey Hirsch, the pianists Merle Koch or Stan Wrightsman, and the bassists Don Bagley or Morty Corb, and it played the Hollywood Bowl in 1963. He appeared on The Tonight Show Starring Johnny Carson 56 times, was voted best jazz clarinetist in the Playboy readers' poll for thirteen years running from 1962, played at the White House five times, and performed for Pope John Paul II during the pope's 1987 visit to New Orleans.

In the spring of 1960 he opened the French Quarter Inn at 800 Bourbon Street, where Frank Sinatra, Robert Mitchum, Robert Goulet, Keely Smith and many other entertainers dropped in; when the singer Brenda Lee sat in with the band, the result was a duet album, For the First Time (1968). Eight years after the Inn opened he began leading a ten-piece band at Pete's Place on Bourbon Street, and in 1977 he moved his club to the Hilton Riverside hotel, where he played four nights a week until closing it in 2003 before a packed house. He then played twice a week at the Casino Magic in Bay St. Louis, Mississippi, where his home was destroyed by Hurricane Katrina in 2005. After heart surgery in 2006 he returned for the New Orleans Jazz and Heritage Festival, at which he had appeared some forty times; his last show at that casino, by then renamed the Hollywood Casino, was on December 8, 2010, and he was mostly retired when he returned to help reopen the resort in 2014. He also founded the Half-Fast Walking Club, a freelance marching group that parades on Mardi Gras Day, and he was its best-known member.

Fountain married Beverly Lang on October 27, 1951, and they stayed together for sixty-five years; they had two sons, Kevin and Jeffrey, and a daughter, Dahra. He passed away of heart failure at his home in New Orleans on August 6, 2016, at age 86, after time in hospice care, and was buried at Metairie Cemetery. Loyola University New Orleans gave him an honorary degree in 2006, and he was inducted into the Louisiana Music Hall of Fame on March 18, 2007, and the Delta Music Museum Hall of Fame in Ferriday, Louisiana, on April 5, 2008.

Fountain's clarinet sound was sweet and fluid, and woodier than most because he played crystal mouthpieces from 1949 on; the first was Irving Fazola's own, given to him by Fazola's mother after the older clarinetist's death. The Guardian described his style as Fazola's rounder tone with the drive of Benny Goodman added, and called him a popularizer of traditional jazz who was often ignored by more highbrow critics, comparing his place in American musical life to that of Acker Bilk in Britain. He was a white New Orleans Dixieland player in the line of Fazola, working a repertoire of standards, blues and marches with a small group, and he stayed with the sidemen and songs he was comfortable with. The television fame is part of the story, and so is the range of the recordings: of the more than a hundred LPs and CDs under his own name, some are straight Dixieland and many are instrumental pop albums, among them a Bert Kaempfert program, that Wikipedia describes as only peripherally related to jazz. His jazz standing rests on his club work, the Dixieland albums such as the Coral sets with Al Hirt, and his festival appearances. In 1997 the critic Doug Ramsey included him in a JazzTimes list of underrated musicians, praising his ear for harmony and his command of time.