Ehh. Orders of magnitude, plural? Several hundred km/h? That's a stretch. These are golden eagles, my favorite kind of bird. Their diving speed is around 220-250 km/hr, and their horizontal speed is around 40 km/hr. They will speed up horizontally to catch prey, but this is typically only up to about 90 km/hr.
I've seen UAVs kill birds before though, and it's always a horrifying scene, reminiscent of the plucky character in a dystopian sci-fi movie meeting the all-powerful violent crusher of doom. Moderately powerful UAVs can easily resist birds. Even an off the shelf DJI Phantom 4 can - with stock everything - go 72 km/hr horizontally. I'd bet the eagle could catch up to it, however: the problem comes when the bird meets drone.
Every bird-drone incident I've seen is usually an instant kill (or comes close) for the drone, simply because most of the surface area of the drone is covered by four spinning propellers. The tips of these blades are going several hundred miles per hour, and the area of the top not covered by blades is only a few square centimeters covered in smooth, hard to grip plastic. Now you're telling me that a huge bird (that has a wingspan longer than most humans are tall) can grab onto this tiny place without becoming mincemeat? If the blades are carbon fiber, there's a good chance they won't break upon cutting the bird in half.
I've worked with drones enough to know what will and won't stop them. A bird won't: it'll brush the blades and fall to the ground in a bloody mess. A bullet will. Bullets are tried and true technology, we know how to use them, they're not ridiculously expensive, and they will certainly take down any drone of reasonable size.
This is PR, plain and simple. There's no other explanation for it, unless France's air force is hilariously incompetent, which I would doubt.