This is what I found:
Carl Vilhelm Marius Bendtzen, born: 21 Nov. 1879 in Horsholm, Fredriksborg, Denmark. Christened: 7 Dec. 1879 in Horsholm. Parents: Lars Bendtsen and Petre Karen Marie Andersen. (Source: International Genealogical Index [IGI] on FamilySearch.org, extracted record information from the Parish of Horsholm, film # 48677)

This couple had a another son:
Ernst August Georg Bendtsen, Christened: 4 April 1886 in St. Olai Church, Helsingor Parish, Fredriksborg, Denmark
Parents: Lars Bendtsen, and Petra Karen Marie Laura Andersen (Source: IGI, parish record of Helsingor, film # 306694)

I also found this family on the 1880 census of Horsholm:
Lars Bentzen, 23 years old, farmer, born in Horserod, Fredriksborg.
Petra Karen Marie Laura Bentzen born Andersen, age 28, born in Naerum Lyngby, Copenhagen, Denmark.
Christian Harald Rasmus Olsen, age 1, their child, born in Vedbaek Sollerod, Copenhagen.
Karl Vilhelm Marius Bentzen, age less than 1 year, born in Horsholm.
(Source: DDD)
(Because the one year old child has a different name, he could have been from his mother's previous marriage--just a thought)

This could be the Carl, brother to Catherine Christine Bentzen. I can't find Catherine Christine Bentzen anywhere in Fredriksborg county. And she should have been listed with this family, unless she was a foster child, or whatever.
I hope this helps!
Lori B