So if Australia send military support to Paris Macron will send his army to help us oppose China in the pacific as a return favour...... I guess they might but Europe has enough of its own problems. I dont think my side should get too involved in another European war though because we will be stretched in the Asia Pacific if things kick off.
I guess France would have some colonial african units with Jungle warfare experience with time on their hands now they got booted from their opressed colonies. They could be useful.
I doubt the major cities of Russia would be too concerned with the Australia/France military exchange program, i dont think it will have the dramatic effect you outlined. I think you are way off the mark over the top, they will barely notice.