He was born in Pézenas, in the Hérault department of France. A brilliant scholar, he prepared for the entrance exam to the Centrale (engineering school) and Sup-Aero at Montpellier, but was conscripted into the Youth Building Projects in 1942 and sent to Germany in 1943 for compulsory work service. He escaped the same year, and found work as a diver in La Ciotat, a suburb of Marseilles, in 1944.
In 1946, he married Colette Maclaud. They had two children, Ticha (born 1948) and Jacky (1950).
His first published work, Les douze chants d'un imbecile, appeared in 1951. He moved to Paris and opened a fashion and baby clothes shop, still writing and producing plays. Later, he switched to being a fitter of TV aerials and began singing.
His fame grew when the actor Bourvil sang Lapointe's song Aragon et Castille in the 1954 film Poisson d'avril. In 1960, film director François Truffaut offered him a part in Tirez sur le Pianiste where he played Framboise, accompanied by Charles Aznavour on piano. This marked the start of a career that saw Lapointe perform at major venues throughout France. His joyful character led him to build friendships with French stars Anne Sylvestre, Raymond Devos, Jacques Brel and Georges Brassens.
Lapointe was also a mathematician, and developed the bi-bi-binary system (also known as bibi system) in 1971.