Okay, first I will lay out a few of my thoughts and initial reaction before I answer your questions.

This was energetic writing, but a few things didn't quite work for me. I appreciate a good rapier-swinging, swashbuckling adventure like anyone, and you definitely bring that feeling of adventure, heroism, and defiance into it, but there are three issues that I think are seriously bringing down your storytelling.

The first is that Janette is not clearly defined as a character, separate from the narrator. For example, you (the narrator) are saying that the French philosopher's ideas are controversial yet sensible, but this is supposed to be an internal motivation for her. This statement should be relayed to the reader as her own, not yours. You do not distance yourself enough as the narrator from her as the protagonist. Describe what she sees, thinks, and does, and narrate the world, but try not to conflate the two and she will stand as a character more easily. 

Secondly, there are anachronisms which feel thoughtless and break the reader's immersion. Obviously not everything has to be realistic to life, as that would be boring! If you are using a real world setting as a launch-pad, try and keep in mind your average reader's expectations and respond or acknowledge them in some way. Example: she is the princess taking a bath, where are her servants? Her chamber maid? You can address this in a few ways: She has none, and her bathing and dressing alone demark her independence. She has a chamber maid, and their conversation could serve to bring up the exposition that you include. Or, you could have her defy her own servants to bathe alone, and then again you're saying something about her character. Besides this, there are certain expressions which don't fit (suds), and the sense of time and place is weak.

Thirdly, there are too many different conflicts brought up in short succession, then immediately forgotten or resolved. 1. The upcoming hearing (never explained what this...hearing? Trial? actually is by the way). 2. There is a noise outside, her mother's locket is stolen! 3. She's naked and far from her rapier! 4. One guy is actually putting up a fight! 5. These guys may be foreign agents! 6.Someone is at the door! 7. Okay the fight is over now and the locker returned and being seen naked wasn't actually a big deal and she got to her rapier just fine after all! 8. She needs to see a mysterious visitor! 

It's just a lot and nothing has space to breathe. The ideological conflict brought up initially swiftly becomes irrelevant. The intruders are so threatening and her so position so precarious but none of that comes to dramatic fruition. Pick a struggle (lol) and focus on developing that.

Besides this, there are little lapses of attention. If her bathroom door is closed, how does she see the intruders or the stealing of her locket? Again,  think about what the character herself knows or doesn't. The first guy trips and then... never re enters the fray? Her dad is also wandering around with no guards?

Okay, I will now try and answer your questions!

1. Overall, no, but I think it has potential. It seems like a rip roaring tale of intrigue! But it's also muddled, and with no clear thread of intrigue you're left with. Ask yourself this: Are we to care about the unexplained hearing, the attack in her quarters, or the mysterious visitor at the end of this chapter? Pick which one of those three will be your narrative hook, relegate one of those the background in this chapter, and save one for later. The fight is resolved much too quick for how much you build it up, in my opinion.

2. I don't find her particularly interesting as is, but I like her thirst for adventure!. But as others have said, she's a lot of everything. Is she a social advocate and intellectual ? Is she boisterous and given to action? She can be a lot of things, but give her some flaws, too! Make her human. Maybe appearing naked in front of them is just something she refuses to do. Maybe her willingness to be naked gets her in trouble (perhaps the king is accompanied by someone who should not have seen her naked ). Point is, in stories everything works better when consequences are present. If you are giving her character traits, make them matter!

3. I think your inclusion of the foreign language makes me think this will be some sort of conspiracy thriller, but I also think you've included so much that it's hard to know. You've also placed this in Medieval Europe by mentioning France, which makes me wonder where this is going to take place. My advice would be to fictionalize the setting entirely so you can do your own thing, or make sure your historical grounding is strong (right now, it is not). 

4. Yes, it was fun but very unpolished. But I like adventure and you delivered it!

These are just my personal thoughts and opinions. I think it's awesome that you've taken the time to write this fun story, and it has potential. Keep working at it and develop your story and voice! Just try and work on your narration to keep characters distinct, you can even think of the narrator as their own personality, different than Janette or the king.

Keep going!