Speaking together to reporters for the first time since their story was published two weeks ago, Dyrk and David Hesshaimer and their sister, Astrid Bouteuil, said they don't want money, just acknowledgment that Lindbergh is their father.
"That is the most important thing we have to repeat," the eldest sibling, 45-year-old Dyrk Hesshaimer, said in English.
The Hesshaimer children have offered no proof beyond a bundle of 112 letters Lindbergh allegedly wrote to their mother, Brigitte. They also have childhood photographs with the famed aviator and their own recollections of the tall, lanky man who they knew as Careau Kent.
Pressed about offering more concrete evidence, Dyrk Hesshaimer said: "We are open to a genetic test." The family's lawyer said they would pursue a DNA test later this year.
The siblings have not contacted the Lindbergh family in the United States, which has refused to comment on their claim. Lindbergh had six children with Anne Morrow Lindbergh, and the oldest, Charles Jr., was kidnapped and murdered in 1932 at 20 months of age.
The Hesshaimer children, born between 1958 and 1967, said they didn't realize Lindbergh was their father until the early 1980s when Bouteuil, the middle child, began asking questions.
After discovering a bundle of letters allegedly written by Lindbergh and addressed to her mother, Bouteuil confronted her and was finally told that Kent was actually Lindbergh.
The children promised to keep the secret until after both their mother and Anne Morrow Lindbergh were deceased. Both died in 2001.
Lindbergh's Pulitzer-prize winning biographer, A. Scott Berg, told The Associated Press when the siblings made their claim that it would have been out of character for Lindbergh to father the siblings.
The Hesshaimers say Lindbergh met their mother, a Munich hat maker, and fell in love in the mid 1950s when he spent much of his time traveling the globe.
Lindbergh would visit the family once or twice a year when the children were young, staying for five days to two weeks, Dyrk Hesshaimer said, and their mother forbade them from discussing their father outside of the family.
"We quickly built up a close relationship to him," he said. "We didn't have the time together with him that other children had with their fathers, but when he was there he concentrated very intensively on us."
Bouteil, 43, recalled long breakfasts where her mother and Lindbergh would talk for hours, and of the people he'd met.
"I knew that he was something special," Dyrk Hesshaimer said. "He had knowledge about U.S. politics that wasn't in the TV news at the time."
Their mother received what would be her final letter dated Aug. 16, 1974. It read, "I am losing energy everyday. My love to you and the children, all I can send."
Brigitte Hesshaimer later read in the papers that Lindbergh had died of cancer on Aug. 26, 1974 She told her children simply that their father was dead.