That does not correspond well, not at all I’d say.

(Cambridge Dictionary)
like a ton of bricks very strongly or forcefully:
♦ If Dad finds out what you’ve been doing, he’ll come down on (= punish) you like a ton of bricks!

There is not that idea of force in the expression "moineaux piaillants" but rather that of bustling activity. Moreover the image is not complete and in English a "complete" image will be needed (comme une nuée de moineaux piaillants se jette sur des semences ou des graines qui leur sont jetées).

I can’t think of an idiom; as "comme une nuée de moineaux piaillants" is not an idiom either why not use a similar image?

Here are two possibilities.

• We threw ourselves on the sixth one as a swarm of chirping sparrows on the crumbs on a pavement.

• We threw ourselves on the sixth one as a swarm of buzzing bees onto an intruder.