According to the flight crew, the airplane was descending to land with the autopilot configured to intercept a managed flight path profile. The airplane was descending in "Vertical Speed" mode at 500 feet per minute, with the airspeed set for 300 knots. As the airplane approached the profile, the crew selected "Managed Descent" mode and the airplane nosed over rapidly to intercept the descending flight path. The first officer checked the altimeter setting and then noticed that the airspeed indicator was approaching the maximum allowable airspeed; he then deployed the speed brakes to about 50%. Simultaneously, the captain took control of the airplane, disengaged the autopilot, and pitched up to avoid an overspeed condition. The crew then reset the automation and commenced a deliberate slow down. Shortly thereafter, the cabin crew called and advised that one of the flight attendants was injured during the maneuver. A flight attendant who was securing carts in the aft galley was hoisted into the air and landed on her left foot, fracturing her ankle. The remainder of the flight continued without incident.