I'm not sure, but I think that there can be varying degrees of parole-like situations. Not really a parole but transferred to correctional centers with programs that are focused on making a transition into the community. The parole board can make all kinds of recommendations.
The earliest version of this statute that I could find quickly is 2006.
La. RS 15:1111 Work Release Program
A. The Louisiana Department of Institutions is hereby authorized to establish and administer a work release program for inmates of any institution under the jurisdiction of the department.
B. The department shall establish rules for the administration of the work release program and shall determine those inmates who may participate in the release program. Any convict sentenced to imprisonment at hard labor shall be eligible at any time during his sentence to participate in the work release program, subject to the provisions of this Part....
I.(1) Notwithstanding the provisions of Subsection B above or any other law to the contrary, any inmate who has been convicted of first degree murder (R.S. 14:30), second degree murder (R.S. 14:30.1), aggravated rape (R.S. 14:42), attempted aggravated rape (R.S. 14:27 and 42), forcible rape (R.S. 14:42.1), aggravated kidnapping (R.S. 14:44), aggravated arson (R.S. 14:51), armed robbery (R.S. 14:64), attempted murder (R.S. 14:27 and 29), attempted armed robbery (R.S. 14:27 and 64), producing, manufacturing, distributing, or dispensing or possession with intent to produce, manufacture, distribute, or dispense a controlled dangerous substance classified in Schedule I or Schedule II of R.S. 40:964, and persons sentenced as habitual offenders under R.S. 15:529.1 shall be prohibited from participation in the work release program except during the last six months of their terms.
http://law.justia.com/codes/louisiana/2006/145/78843.html
Aggravated sexual battery is not listed above. There's a lot more at the link. The statute has been revised twice since 2006.
I'm not sure that Avoyelles Men's CC had a work release program in 2006-08, though.
http://www.doc.louisiana.gov/view.php?cat=8&id=55