Broken bottom bracket?
The bottom bracket is not damaged, the left hand crank arm is.

You have a 'two piece' crank where the right side crank is permanently attached to a steel axle, and the left hand crank clamps onto the axle with two pinch bolts. The axle has small splines cut into it where the crank clamps on and the crank has corresponding splines cut into it.

for the crank to come loose and rotate on the axle the pinch bolts must have been loose. You can re-align the crank and re-tighten the pinch bolts, but the crank is likely to move again because the splines in the crank will have been damaged when the crank rotated on the axle. The axle is made of steel but the crank is softer aluminum alloy.

To fix this you need to replace the left hand crank, which means effectively replacing the whole crankset as left hand crank arms are not generally available individually, although you might be a able to find a matching left hand crank arm on Ebay.

I believe the Trek FX 7s used a Shimano R460 crank, which is a lower-end, relatively inexpensive model. Any Shimano Hollowtech II road crank with matching chainring sizes and crank arm length will be a drop-in replacement.