Short answer. Not while civil interdiction runs. That accessory penalty deprives the offender of parental authority for the time of his sentence, along with guardianship and marital authority. It is tied to the penalty rather than to the conviction as such, so which penalty the court imposed decides the question.
What the law says
Civil interdiction shall deprive the offender during the time of his sentence of the rights of parental authority, or guardianship, either as to the person or property of any ward, of marital authority
Revised Penal Code, Article 34 — Civil Interdiction Explained. Read the full provision →
Parental authority heads the list
Article 34 provides that civil interdiction shall deprive the offender during the time of his sentence of the rights of parental authority, or guardianship, either as to the person or property of any ward, of marital authority. Parental authority is named first, and the deprivation covers both sides of it — decisions about the child's person and the administration of a child's property. The phrase during the time of his sentence is doing real work: this is a suspension bounded by the term, not a permanent severing of the parent-child relationship.
It follows the penalty, not the verdict
Civil interdiction is an accessory penalty that the Code attaches automatically to certain principal penalties. The judge does not impose it as a separate item, and it does not follow from every conviction. So the question "does he still have parental authority" is answered by reading the dispositive portion of the decision, identifying the principal penalty, and checking whether civil interdiction is among the accessory penalties that go with it. A sentence below that threshold leaves parental authority formally intact, however long the parent is away.
Somebody still has to raise the child
Losing authority in law does not answer the practical question of who now decides for the child. Where one parent is under interdiction, authority is ordinarily exercised by the other. Where there is no other parent available, family law provides for authority to pass to other persons and for guardianship to be constituted through the courts. Those are separate proceedings with their own requirements, and they are where questions of custody, schooling, consent and the handling of a child's property are actually settled.
The criminal case is not the only route
It is worth knowing that family law has its own grounds for suspending or terminating parental authority, and they operate independently of anything in the Revised Penal Code. A relative worried about a child's welfare is not confined to whatever the criminal sentence happens to produce. Whichever route is in play, the documents that matter are the judgment showing the penalty imposed, the child's birth certificate, and any existing custody or support order. Take those to a lawyer before making arrangements that assume authority has passed.