After just two years with Sochaux, he signed a semi-professional contract with Basel and stayed with them for ten seasons.
Laufenburger joined Basel's first team for their 1964–65 season under the Czechoslovakian head coach Jiří Sobotka.
[1] Fortunately it was only a small injury, just ten days later on 9 September, he stood in goal to play an Inter-Cities Fairs Cup match in the St. Jakob Stadium and his team won 2–0 against CA Spora Luxembourg.
With the score at 1–1 after 88 minutes play, referee Karl Göppel awarded Basel a controversial penalty.
After the 2–1 lead for Basel the Lausanne players subsequently refused to resume the game and they sat down demonstratively on the pitch.
Laufenburger's nick name was "Bolle", not only to his family and friends, but he also called so by the Basel fan culture.