What is the ruling of Islamic law on receiving funds in different currencies from a friend in Europe, then distributing them to their rightful recipients here in different currencies after deducting a commission, without a direct exchange taking place each time? Is this transaction considered permissible, and am I assisting my friend in sin?

This transaction is impermissible because it combines agency (Tawkil) with currency exchange (Musarafa), and for Musarafa to be valid, immediate possession (Al-Taqabudh) is required, which is absent here. You are not permitted to undertake the aforementioned work due to its assistance in a forbidden act. To correct the transaction, immediate possession must occur between your friend and the client, either actually or constructively, or by the client appointing someone to take possession on his behalf in the other country at the time of transfer.