They can send bags anywhere they want. The line about being standby was pure BS. Even if the bags had been sent to LGA, a file should have been created at JFK. If agent refused you needed to ask for a redcoat/manager. You could also call DL who then would get someone in baggage on the phone. If the bags had been sent to LGA (system should see you flew to JFK and automatically reroute) they could either;

Option 1, pay for a taxi to bring you over, allowing to pickup yourself, and pay to taxi you back.
Option 2, LGA puts on plane to ATL, DTW, etc and then onto JFK if bags could arrive in time for your CDG flight
Option 3, same as 2, but instead of sending onto JFK from ATL, DTW, etc, send onward straight to CDG from ATL, DTW, etc.

For option 3 to work they would've required the file reference from JFK. Otherwise they couldn't send the bag to CDG. This is due to positive bag matching and CDG being a separate reservation.

Sadly they will not send bags by taxi between LGA/JFK without the passenger. I had this issue on the 1st.. They put my bag on earlier flight to LGA, after rerouting my from JFK to LGA due to weather in ATL. My LGA flight got cancelled and they rebooked me to fly to JFK on 2nd. I was flying out to NZ on Latam via SCL at 1845. ATL manager called to have bags sent to JFK. They flat out refused. Instead they'd send back to ATL on one of the early morning flights. Of course they screwed up and didn't. Despite a pissed off ATL manager calling, they still refused to send to JFK. One seat opened on the 1230 departure to LGA. They rebooked me to LGA, paid for taxi to take me to JFK, and issued a travel voucher of $200 for the screwup. Made it into LGA on time, then had to go bag office hunting! They knew what flight I was coming in on and were to have bags ready. No one even knew which office (LGA for some reason has three bag offices) bags were in. It of course was the farthest, meaning had to goto ALL three. By time found it, and took taxi to JFK, I MISSED CHECKIN by 20 minutes due to traffic. DL accepted fault in the mess. JFK agents were shocked how badly LGA dropped the ball. They got Latam to release control of their ticket (this was the return portion of a NZ-US J sale) and rebooked me JFK-LAX-SYD-AKL as there was no Latam J for at least four days. Got to fly VA J class (booked as DL codeshare) LAX-SYD and NZ J class SYD-AKL (booked as VA) on the 777. (Agent I dont believe noticed the VA flight was really a NZ codeshare)

ETA;

Your number three point confused me. However I believe you were trying to say the bags came into JFK later that night. Is that correct?

Since they did goto JFK why didn't you just wait and pickup next day when went to checkin for Paris?