You can do this without dropping any of your European segments if you go back to HKG after SIN, thus using your fourth Asian segment, and then take the daily CX flight from HKG-CDG.

It looks like you have decided to do the AA Gold and Platinum challenges. Flying business, you should make PLT after the DXB-LHR segment. The challenges are based on Q-points, not flight miles. Traveling business class multiplies the actual flight miles by 1.25 to arrive at Q-points. CDG-HEL-LHR-DXB-LHR is a little over 9,000 miles and puts you over the 10,000 Q-points required for PLT. Congratulations!!!