But does that require different skills than an accountant has or even a lawyer ? Because those contracts involve legal issues too, right?
It depends, in France a lot of agents are in fact solicitors(notary, lawyer, jurist) specialized in sports business, so in that case you don't need someone different than your lawyer who calls himself an "agent". But you need someone specialized in sports, you can't just hire the first lawyer you encounter, for example a company who wants to make a merger will hire a specialist in merger.
Also you don't have to monthly pay an agent, you can also only hire him when you are in negotiation, he will provide you legal support and advise during that period and after you just part ways, in that type of situations the agent take a cut on the signing bonus.