Given that the leaked Overwatch: Uprising (or Insurrection) video was from PlayStation France, a translation's probably required for what's actually said for those of us in English-speaking territories.
"Morrison here: London has been attacked, King's Row has fallen. We are in the middle of an open war."
Mercy(?): "Hundreds have died, and a few thousands have been hurt."
Reinhardt: "Willhem reporting. We will save as much lives as we can."
Reaper(?): "Blackwatch agents are noticing important fortifications. Area 0 is in control of the zone."
Torbjorn(?): "Let me, the expert, do what's required. Response team, we're counting on you, and take care of the new recruit."
Tracer: "You can count on me, chief!"
Torbjorn: "Be careful"
Reinhardt: "I'm moving the payload!"
The trailer was leaked over the PlayStation France YouTube channel, and quickly removed. Before then, though, we nabbed everything we could about the upcoming content update. The original leak was before then, when the Xbox Live update used some of its art assets for the Overwatch: Origins storepage. Of course, all the skins were technically "leaked" in the officially launched comic.
The new Overwatch event, either called Uprising or Insurrection, comes April 11 -- tomorrow. Hope you've stashed aside some credits!