Here's the most recent update:

I checked both my parents in at exactly 30 hours before departure. Couldn't print BPs, but managed to change seats for IAH-CDG as well as getting seats for CDG-BUD. On the A332 for IAH-CDG, 4 economy rows (Row 21-24) were opened up at this time. Row 19 and 20 don't show, so can't switch to those. So, I moved them to Row 21.

For CDG-BUD on an A319, the chart shows Row 14-25, but 14 and 15 (over the wing) show occupied. So, I got them Row 16. Seems like Row 1-13 are so-called "business" seats.

They got Seq #1 and #2 for both flights.

Instead of the BP, a confirmation is printed, which says one has to go to counter to get real BP latest at 1 hour before departure.