Traditionally this is high season. Not sure about the particular route, but I would be surprised if it was a half empty flight.
ET check in agents always allocate seats from front to rear, so in order to stand a good chance of a free middle seat, make sure you choose a row in the far back of the plane. Also, do the trick where you book aisle and window. Very few people will pick a middle seat if they have another option. And in case someone gets the middle seat, chances are they'd be very happy for swap for one of your seats. It's a classic trick when traveling two people together. If one of you are Star Alliance gold, it increases the chances of a free seat next to you.