Also, the 7th Cavalry, Company A had a Captain James C. Murphy whose wife applied for a pension.
I have pasted these records below.
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Applicant Information & Name Variations:
DEMARY, EUGENE
Parish: Vermilion -- Pages: 6
DOMARY, EUGENE
Soldier Information & Variations:
DEMARY, EUGENE
State: LA
Branch: Cavalry
Unit: 7TH Regiment
Company: Company A
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Applicant Information & Name Variations:
MURPHY, LAURA (DELAHOUSSAYE)
Parish: Orleans -- Pages: 8
Soldier Information & Variations:
MURPHY, J. C.
State: LA
Branch: Cavalry
Unit: 7TH Regiment
Company: Company A
MURPHY, JAMES C.
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Also, there is a short biography of Eugene Demary published in the year 1891 which states, "Mr. Demary was a soldier in the late war, having enlisted in 1861 and served until May, 1865", but does not state the name of his regiment.
The biography can be found at the following link:
http://files.usgwarchives.net/la/vermilion/bios/demary.txt
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I am not certain whether E. L. Demarry who served in the Crescent Regiment and Eugene Demary who served in the 7th Cavalry is the same person, perhaps the pension application would answer that question.