I hope so, because to capture protected species in the wild is a crime.

In any case even if you can keep an endangered species in captivity in a few special cases, you still could not deliberately put in danger the life of those captive species, because is not a cool toy, is a protected species by both the european and also the french laws. It does not matter if hatched for this or for that. Is still illegal. You can't even let fly freely this species in a public space like a city without breaking the law.

For USA see: The Bald and Golden Eagle Protection Act (16 U.S.C. 668-668d)

In European community "Member states shall prohibit, for species in Annex 1 (that includes Aquila pomarina, Aquila clanga, Aquila heliaca, Aquila adalberti, Aquila chrysaetos, Hieraaetus fasciatus and Hieraaetus pennatus among other species) the sale, transport for sale, keeping for sale and the offering for sale of live or dead birds and of any recognisable parts or derivatives of such birds". Also eggs. And of course to deliberately annoy or harm this species is strictly forbidden. See directive 2009/147/EC