I'm trying to figure out HOW this pairing would come about, I'm assuming that Josephine de Beauharnais dies much earlier than in RL to help kick-start this TL.
The POD...
The Plot of the rue Saint-Nicaise was a bit more successful than RL, instead of simply injuring her daughter with a few shards of glass, the explosion caused more damage, or simply a twist of fate caused Josephine some injury that killed her. Explosions are unpredictable things after all, any one number of things could have caused things to be much worse than RL.
In RL, Martha Jefferson lived in Paris from age 12 to 17, so she arrived (at minimum) in 1813... Napoleon became Emperor on Dec. 2, 1804, and his first exile happened in 1814...
The only way that a marriage could happen between these two is if A) Napoleon's return to power was more successful, i.e. he won Waterloo, and B) Either his new Habsburg wife, Marie Louise either died or he divorced her due to abandonment, and THEN married Martha Jefferson (which entails a prior relationship between the two).
If Napoleon can defeat the forces of Europe at Waterloo, and do so in a manner that really humiliates and breaks them, then MAYBE he can stay in power in France long enough to consider getting a new Empress, especially if Marie Louise refuses to return to him and he worries that his son will die before him.
This relationship is quite the longshot, but it could still be done in a semi-plausible way.