I don't see a pension application for him but I found this using Google...
PIERRE EDOUARD ARCENEAUX was born 1838 in Opelousas, LA, and died 1880 in Opelousas, LA. He married JUSTINE BERTINOT April 23, 1867 in St. Landry Parish, LA
I tried to find a email or some other way of contacting the webmaster of that page but they have no contact information listed. Anyway, if he did indeed pass away in 1880 that would explain why he never filed for a pension. It also shows Justine may have remarried or died herself before the State of Louisiana began issuing pensions. She may also have simply been well off financially and thus not elgible for a pension.
Do you live in the Opelousas area? If so I can put you in touch with some folks who may be able to help you out.