[2] A central midfield playmaker, Holtz started his career at Red Boys Differdange before joining Avenir Beggen for the 1992/1993 season.

With Avenir Beggen he immediately won two successive league and cup doubles and he himself claimed the 1993 Luxembourgian Footballer of the Year award.

With Etzella, he immediately won promotion to the Luxembourg National Division in his first season in charge.

Holtz made his debut for Luxembourg in an October 1991 friendly match against Portugal, which surprisingly ended in a 1–1 draw.

Holtz's son, Kevin, is also a Luxembourg international footballer, making his debut under Luc.