[Edited] There is sometimes a train that is direct from Interlaken to Paris, probably in early morning, but most departures require a connection at Basel. Currently, I can find the direct Paris-Interlaken departure at 18:30 most days, using either the Lyria or the DeutscheBahn schedule links, but I can't find the direct train in your direction of travel for any spring travel date that I've tried.
For most departures, Basel-Paris is the more important piece to book with advance discount, just as long as you plan in adequate time to reach Basel. You can buy the Interlaken-Basel ticket separately, including at a train station in Switzerland, or you could use a Swiss Travel Pass for that trip, if you're getting one.
P.S. Although the overview page indicates that the direct train runs both ways ( <> ), as it has in the past, the PDF schedule indicates that it's now running only in the direction departing Paris.