Almost certainly the Empress tragically dies in 1809 or 10
Please don't buy into the myth that Bonaparte and Josephine was a love match
when they first met Bonaparte - then regarded even by the Republicans as a parvenue half Italian rustic - had arranged a financially advantageous engagement with the daughter of a rich merchant
Josephine was the Widow of an aristocrat who had turned republican to save his life but was later executed for treason.
She had saved her own life by becoming the mistress of a series of important republicans, culminating in Barras, then in charge of France.
When she became a nuisance to him Barras made a deal with Bonaparte to take her off his hands in return for a promotion
(the existing fiancee was literally left with an unused trousseau)
Josephine faced with the prospect of banishment to the outer dark agreed
but probably expected to become a widow again in short order as Bonaparte's new mission was expected to disastrous.
Against the odds , Bonaparte survived and prospered and Josephine as a canny survivor clung to his coat tails.
She was a beautiful woman and like most of her family sexually uninhibited so I'm sure Bonaparte enjoyed her bed
But she was never enough for him.
Throughout his marriage Bonaparte was repeated unfaithful, seducing women for both personal and political reasons.
He fathered several bastard children so knew he was fertile while Josephine, despite having children by her first husband, now appeared barren
In OTL as soon as he thought there was a chance of a political advantage,
Bonaparte discarded Josephine and seized Marie of Austria as a war captive bride ... or should I say brood mare.
in this ATL, if Josephine had given him legitimate children Bonaparte could not simply divorce Josephine
So he has two alternatives:
1) Frame her for adultery and divorce her but that would call his manhood into doubt
2) Have her quietly succumb to a (relatively) swift illness and hope to reap some sympathy as a widower with young(ish) children
The man that murdered so many of his political opponents - including his best chief of staff when he refused to break his word of honour and join Bonaparte again in 1815 - will surely chose the second.