The civil records of Luxembourg can be found online at Familysearch.

The birth record of Clara Duscheng is at Image 429 of the list Weiler-la-Tour Naissances 1796-1890, number 27, October 13th 1840 (at the left side on the bottom). Her parents were Johann Duscheng (a 33 years old day labourer) and Anna Maria Rovin.

The marriage record of v and Clara Duscheng is at Image 344 of the list Weiler-la-Tour Mariages 1796-1890, number 2, January 16th 1861 (at the right side),

According to the marriage record, Nicolas Demuth was born May 9th 1832 in Wormeldange, his parents were Nicolas Demuth (deceased before 1861) and Anna Maria Schmit.

I can look for additional informations at the National Archives of Luxembourg.

Sincerely yours,
Claude Vanolst