Have you tried resetting your key fob? This must be done when you change the battery in your key fob, and may well be necessary when you change the big battery too.
I have the 406 handbook in front of me now. It's written in Dutch, which I understand perfectly. I will translate all to English for you (my native language).
If the remote control doesn't work after the replacement of the battery, this must again be reprogrammed.
If lamp "B" only one time glows, or doesn't glow at all if the button is pressed, change the battery.
PROGRAMMING THE REMOTE CONTROL KEY FOB
1. Push on button 'A' (in the center of the key) and hold down, until little lamp 'B' blinks. ('B' is also on the fob)
2. Let the button 'A' go. The blinking lamp burns constantly.
3. Push 2 times on button 'A' in the immediate vicinity of the auto.
4. Set the ignition contact switch ON for at least 3 seconds.
....(I believe this means insert car key and turn it to the "M" position. "M" for accessories ON position. It is not necessary to start the car, in furthest position 'D')
5. Turn the ignition OFF.
The remote key fob now works again.
NOTICE: Don't push the remote control button OUT OF RANGE of the auto. By that, the system can go out of order. In this case, the remote must be again re-programmed.
(It doesn't say what the range is??)
If the remote doesn't work after changing the battery, it must be reprogrammed.
Seek advice from your service-dealer if the problem persists.