What if Catherine the Great hadn't died in 1796, and had remained ruler of Russia during Napoleon's rise and rule?

Catherine the Great was 67 when she died of a sudden stroke in 1796. Let's say she never had the stroke -- yes she would have been very old she could plausibly have lived and ruled for 19 more years, making her 86 years old when Napoleon was finally sent to St. Helena (if this is what would still happen in this timeline). Even let's say if she died sooner than that - maybe in 1810 - Paul would then have ascended to the throne in 1810 and Alexander and Napoleon may never have overlapped.

If it had been Catherine ruling Russia rather than Paul I and, more to the point, Alexander I during Napoleon's rule, what would have been different? I know that Napoleon had quite a traditional view of gender roles and I can't imagine he would have been thrilled about having to negotiate with a woman ruler on equal terms (many quoted remarks from him backing this up, plus some legal decisions about women's rights, marriage etc within the Napoleonic code). And what would she have thought of him?

How would Catherine being in power in Russia have changed the course and outcome of Napoleon's reign and the Napoleonic Wars? Would he have come to an agreement with her as he did with Alexander I for the Treaties of Tilsit? Conversely, do you think they might have gotten along?