"Well, laughing....7 days only is too short for me for Paris! My last few trips have been between 10 and 14 nights and there are always things I have to put off until the next time. I'd do as Balso says and see what you want to do in Paris and then see how many days."
I also agree with the above, and am joining Pam in laughter! I have never spent less than 7 nights in Paris, but am preparing for my third trip there in May. (It is part of a longer trip elsewhere in France and the Spanish Basque Country, where we have never been.) Paris is our arrival city where we will spend only 5 nights, i.e., 4 full days. I already have serious FOMO about the things we will not have time to do!
Many of the places in Paris that are of interest (described in your initial post) are nearly identical to the ones I visited on my first trip, which was 9 full days in Paris, plus one day trip to Versailles. (BTW, I did this as a solo traveler. I loved every minute and never felt unsafe.) All of this to say that based on your stated interests, you could easily enjoy 7-9 days in Paris (including a nearby day trip or two) and not get bored. Very subjective, of course. For example, for people who do not like large cities and/or museums, 7 days in Paris may be too long, as is the perception of your daughter's friend. But that person's interests are not necessarily yours. It really does depend on what you want, how much time you envision spending in museums, etc. If you are really into art, spending the better part of the day at any of the larger museums (e.g., Musee d'Orsay, Louvre) will be richly rewarded.
A day trip to Giverny is feasible, and it would give you a taste of the countryside that your daughter is seeking. If you want to visit Maison de Monet, it is best to reserve your tix ahead of time since you'll be going in peak season. https://fondation-monet.com/en/
If Paris is your first destination after a transatlantic flight, remember that you won't be able to do much on your arrival day. So, if you only have 8 full days on the ground, you do not really have time for a trip to the south or the Loire Valley. Unless you have an opportunity to stay longer than 9 days for the entire trip to France, I would postpone those farther-away destinations for another trip, when you can really focus and enjoy it. Everything is a trade off.