I hate to burst a lot of peoples bubble here, but Paramore is not that big. Yes, they've had a very nice run this past year and half or so, but honesty, they can't hold a candle to No Doubt's popularity or success. Not to say they can't in the future, but as of right now, no. So it's laughable to think No Doubt would be an opener on ANY tour.
Plus, if this is going to be an amphitheater tour, Paramore would desperately need No Doubt to fill the place. At least the Shoreline Amphitheater over where I'm at. Place is huge.
And it's not like Paramore would get some dinky 25 minute set. I'm sure they would get a full set, they'd just be performing first *OMGSHOCKGASP* BIG DEAL.