I think the likelihood of finding a low-tier award via the Atlantic for this Thursday is pretty low. Do you have to be at work in Paris on Friday? If not, and if you are willing to fly the long way around, I would check availability for LAX-Asia, and then Asia-PAR. This will almost certainly require two separate awards, but if you can get both at the low-tier level, you might be able to get the one-way for about 150K transferred Amex MR points.

Be aware, however, that not all Amex transfers are instantaneous. If you find availability on an Aeroplan partner that does not have surcharges, Aeroplan will put the flights on hold while you are on the phone with them if you immediately transfer your Amex points to Aeroplan.