La. Stat. tit. 13 § 3047
In districts composed of more than one parish, the jurors drawn for the first week of the session shall constitute the jury in civil cases for that week, and those drawn for the second shall serve for the time for which they are drawn, provided, that if the jury drawn for any week of the session do not serve as jurors during that week, they may be required to serve during a subsequent week of any session of the court until another venire is drawn by the commission, unless sooner discharged by the district judge. If a jury be empaneled in any case, and the trial commenced and the week for which the jury is drawn expires, such jurors shall continue to serve in the cause in which they are empaneled, until a verdict is rendered or they are discharged by the court.
La. R.S. § 13:3047