The Council wants you to assassinate the leader of a art smuggling ring to stop them from stealing art for the national museum.
For a quick and easy kill head to the tunnel in the southwest of the restricted zone and stop half way into it. You should see a large statue straight ahead, which the target will stop next to if you wait. Once the target is in sight, hit him with a Phantom Blade headshot and walk out of the tunnel to complete the mission.
A Dramatic Exit
Duc de Barrois uses his influence to have his rivals assassinated and take possession of their property, but the Council wants you to kill him during the theatrical performance being held at the Hotel de Sully.
Make your way to the southwest of the restricted zone to find a small alley that can be used to enter the mansion. Wait for Barrois to enter the lobby and head upstairs before you enter and hide under the staircase to await his return downstairs, where you can sneak up behind him and assassinate him quietly. Now exit out the alley to complete the mission.
Breaking the Habit
A group of thugs are terrorizing the nuns of Filles du Calvaire, so to solve the issue you need to identify the leader and assassinate him.
Make your way to the restricted zone and enter the outer wall and turn left to a second archway. Make sure the Seeker is walking away before you enter and take cover on the inner archway to align a headshot on the leader. Once killed, make your way out the same way you came in to complete the mission.