Head through the doorway in front of you, walking to the left up the stairs. Use Eagle Vision to find and follow the blood trail that the assistants are leaving. Head through to the next set of stairs. Take the ones on the right down. Head into the building in front of you.
Once inside go straight ahead. You can now use Eagle Vision to find your target, La Touche. He will walk between 2 Extremists who block the way otherwise. Just go straight across from where you came in to find a way around them. Use Eagle Vision to track your target. Watch for a smaller passage on the left. Move to the end of it and watch for Le Touche to turn his back. When he does, slip across the opening and keep following him. After that, keep sneaking out onto the street. Once there, stop sneaking and start walking. You cannot blend while using Stealth. First, head for the topple carriage to get some cover to shake off any guards who may have noticed you. After that, walk over to the first crowd and Blend with them. Follow La Touche as he leaves that area. Climb up onto the roofs for the next part to just make it easier. Follow as best you can from above, using Eagle Vision to keep a visual lock on La Touche. This will lead you .