Was it Megan Non-McArdle who said that women are judged by their looks from day one to the grave? Royal would make a good character on Lost, so I see a few possible political effects:
1. French men will swoon, roll over, and play dead while she passes further protectionist measures.
2. Other women will never trust her.
3. Men, at the meta-level, know that beautiful women trick them all the time, so they will never trust their trust in her.
4. She needs to prove she is tough, and that implies hawkish, nationalistic behavior. She will be especially constrained.
5. She provides a national and global public good, but the Modigliani-Miller theorem holds and each part of her persona is evaluated separately, and accurately.
6. She will be an especially effective diplomat on the world stage.
7. No one cares, or is influenced by looks.
8. If the median voter model were true, the President would be so beautiful every election. Some other model must hold.
We haven’t had many beautiful top female leaders, so most of the data is for attractive male leaders; I doubt if the two cases are symmetric. Overall I opt for #8, with a dose of #4 and a bit of #3 and #2.
Wikipedia notes: "For the recent campaign for the Presidential nomination she changed
from wearing dull clothing to stylish suits and reportedly had work
done on her teeth."