My view is that he died in his sleep in the room next to the kitchen, having 'sealed' Anne in their bedroom as the nearest thing he could manage to giving her a proper funeral.
As he drifted off to his final sleep, he imagined Anne in good health, and they 'went out for a walk' together, effectively the moment when he died. I feel that in his own mind at least, this is a hopeful, optimistic belief, another illustration of the power of human love. He believes that he has done everything he can to protect her during her illness, that even killing her was a (desperate) act of mercy to cut short her agonies and indignities. He has prepared her 'death-bed', and then his life is also effectively finished. He lies down and dies, but does so in a positive belief that he and Anne can be together in death (but without any mention of a spiritual or religious Heaven).
When the emergency services break into the flat, the smell is immediately apparent before they break the seals on Anne's tomb. I believe this is coming from Georges' body in the room next to the kitchen - which is open. We never see the crews enter the kitchen or (at that stage) that there is even a room there. We only see the result of Georges' final act of love for his wife.