I don't remember there being a grocery store in Atikokan - you would have better luck buying groceries in Ft Francis if coming from the West, or Thunder Bay if coming from the East.  You could always get fz dr foods from any of the outfitters in Atikokan.

getting a permit starting out of French Lake is just a matter of getting in line there at the ranger station the morning you want to enter (unless the unlikely happens and two other parties are ahead of you that day for the two unreserved spots).  fairly likely to be able to get a permit for a Batchewaung entry as well, especialy if you are flexible and able to start on a weekday.

shuttle?  contact any of the outfitters in Atikokan (just google for atikokan outfitters) and see waht they would charge you for a package - canoe rental and shuttle - alternatively, you could arrange to leave your cycle in US, ad get an outfitter to rent a boat and shuttle you up to Atikokan, and you paddle back to your bike - you would have to have the outfitter meet you at the take out of course, so they could get thier boat back.

what do I think ?   - I think it is gonna be expensive - I did pay for an outfitter to shuttle a group of four from Ely to Beaverhouse Lake entry, and we paddled one-way back to Moose Lake in BWCA - that was in mid-nineties sometime, and cost about $250 at that time, just for the shuttle ride north.

only way you'll find out is to contact outfitters now and ask them how much

I only did a one-way trip that once -mostly I just plan a loop trip and finish back at my truck where I started - lots easier