WI: Francis I takes Bloody Mary as his second wife

If Francis I marries Bloody Mary and Bloody Mary has sons with Francis I, would she still try to take the throne from her siblings, how would she fare in the long term, would she end up in a nunnery after the death of Francis I or she would still take Philip of Spain as her second husband?
 
Mary I of England (b.1516: d.1558) m. Francis I of England (b.1494: d.1547) (a)

1a) Louis de Valois, I of England and Duke of Anjou (b.1535) m. Joanna of Austria (b.1535: d.1573) (a)

1a) Henry de Valois, Duke of Cornwall (b.1556: d.1556)

2a) Mary de Valois, Princess of England (b.1559)

3a) Edward de Valois, Prince of Wales (b.1561)

4a) Miscarriage (c.1564)

5a) William de Valois, Duke of York (b.1567: d.1570)​

2a) Catherine de Valois (b.1539: d.1561) m. Francesco I de' Medici, Grand Duke of Tuscany (b.1541: d.1587) (a)

1a) Bianca de Medici (b.1558)

2a) Isabella de Medici (b.1559: d.1559)

3a) Francesco de Medici (b.1561)​

3a) John de Valois, Duke of Berry (b.1542) m. Dorothea of Lorraine (b.1545) (a)

4a) Miscarriage (c.1544)

5a) Joan de Valois (b.1546) m. Carlos, Prince of Asturias (b.1545: d.1568) (a)

1a) Maria Catalina of Spain (b.1564)

2a) Philip III of Spain (b.1565)

3a) Juan of Spain (b.1566: d.1568)

4a) Miscarriage (c.1566)

5a) Isabella Eugenia of Spain (b.1568)​
 
I'd imagine parliament of the time would have very little interest in the French Queen as England's monarch and would be pushing for her to not be part of the succession. Of course this is not to say that they would make it happen. And if she bears sons, France has a vested interest in the throne.
 
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