Hallyday, 69, had a severe case of "persistent bad bronchitis," producer Gilbert Coullier said.
He denied French press reports the leather-clad rock star developed tachycardia, or a sudden, abnormally fast heartbeat, while vacationing on the French Caribbean island of St. Barthelemy.
With tachycardia, the heart pumps less efficiently than normal and provides less blood flow to the rest of the body, including the heart itself. The increased heart rate also leads to increased work and oxygen demand by the heart.
Hallyday was taken by helicopter Sunday evening to a hospital on the French island of Guadeloupe, near St. Barthelemy, and was later reported in stable condition, the University Hospital of Pointe-a-Pitre said.
Hallyday's son David Hallyday sent out a Twitter message Monday saying: "Thank you so much for your messages, it touches me a lot .. The news is very good, which reassures us enormously. Kisses to you all xo."
Coullier said in a statement the elder Hallyday was "eager to get out [of the hospital]," the French newspaper Le Figaro reported.
Hallyday has been working on an album due for release in November, The Hollywood Reporter said. The singer, known for his Elvis-like style and raspy voice, is scheduled for 22 tour dates starting in October.
The tour "will not be in danger [by this latest incident]," Coullier said.
Hallyday was operated on for colon cancer and separately for a herniated disc in 2009. He suffered complications from the disc surgery days later while flying to Los Angeles from Paris and had emergency surgery at Los Angeles' Cedars-Sinai Medical Center that included being put into a medically induced coma.
Hallyday had his artificial hip replaced last year.
Hallyday has completed 100 tours, had 18 platinum albums and sold more than 110 million records in a career that started in the 1960s.