The starting point for any Louisiana state sentence calculation is the 85 percent rule. Regardless of what the sentence says on paper, Louisiana requires inmates to serve at least 85 percent of their sentence before becoming eligible for release consideration. On a 4 year sentence that is 48 months, and 85 percent of that works out to roughly 40.8 months, so just under 41 months served before any release is possible.
The 15 percent that represents the maximum good time credit is not something that gets added on top of release. It is the reduction from the full sentence that the 85 percent rule already accounts for. He starts with that credit applied and can only lose it through disciplinary infractions. If he keeps his record clean, that 41 month figure is the floor.
Whether anything beyond that standard 15 percent applies depends entirely on what is written in his Judgment and Commitment order, which is the document signed by the sentencing judge. Some sentences include additional program credits or other provisions that could create further reduction. That document is the authoritative source and worth obtaining a copy of if you do not have one already.
On the non-violent offender law you are referencing, that is an important clarification. The major sentencing reforms tied to non-violent offender provisions, including First Step Act benefits, apply to federal sentences only. Louisiana has its own state-level reforms that have been passed in recent years affecting certain non-violent offenders, but whether those apply to his specific charge and sentence depends on the details. His attorney or the public defender's office can review the sentence and tell you whether any Louisiana-specific reform applies to his case.
The split between parish jail and a reentry program is actually a positive structure. The reentry program portion is designed to ease the transition back to the community and typically comes with more flexibility and resources than straight incarceration.