Considering Louis XII died barely three months after his second marriage, it means Mary won't have been pregnant for long. Were people able to detect a pregnancy before the third month* in those times? Just a question, because if Mary Tudor's pregnancy remained undetected, events could take a rather funny turn...
Anyway, with Mary Tudor being pregnant, then her child's gender won't be known until she gives birth to it. This is important because the French will have to wait for her to give birth to know their next King: thus, the moment Louis XII dies, France is under Regency. Mary Tudor, as dowager queen, can claim Regency: France allows Queen Mothers to take regency for their children (it was done several times OTL). However, given the situation, Francis of Angoulême (OTL François Ier), as Premier Prince du Sang** and heir to Louis XII by default, will likely play an important part in the Regency. I can see Mary Tudor and Francis being declared co-regents eventually.
After that regency, all will depend on the gender of Mary Tudor's child. If it's a boy, he will be the next King of France. The regency will remain in place until the boy turns 13 (or 14, I'm no longer sure) by which point he will be declared able to rule alone. This will probably leave Mary Tudor forced to remain in France unless Henry VIII insists otherwise: however, I doubt he would ask her to go home considering his nephew is King of France. Regarding OTL Francis I, he won't disappear from History: via his marriage to Claude of France (he was already married to her before Louis XII died I believe), he is Duke of Britanny jure uxoris. Plus, he holds a number of counties that make him one of the strongest nobles in France: his only rival would be the Duke of Bourbon I believe. Britanny won't be in Personnal Union with France in this scenario, but it will be seen as part of the French Kingdom: I can even see possible marriage with the French Royal family to ensure it remains this way.
If Mary Tudor were to give birth to a girl, then the French succession would remain unchange compared to OTL: Francis I would still become King. The question of Britanny wouldn't show up because of Claude of France being Francis' queen. To sum up: same situation, even if delayed by a pregnancy. What changes is Mary Tudor's fate: will she leave the French court? She was the favorite sister of Henry VIII but her daughter will be considered part of the French royal family. Henry VIII could let her remain in France, thinking she and her daughter could play some important role.
Regarding the question of the English succession, it's a rather tricky one. The child is not ill-place considering he comes right after the children of Henry VIII and Margaret Stuart, but he is also not so well placed considering those two bloodlines. Plus, being French, the English won't want him as King/Queen: the French didn't want an English King and that cause a Hundread Years' War. Who says the English want a rematch in the reverse way?
*If you're wondering why I mentionned the third month of pregnancy, it's because the mother's belly starts to grow & reveal the fact a woman is pregnant.
**First Prince of Blood