Paris Sept 2027 (Looking for suggestions)

If you are planning to go to Versailles and spend a day in the Champagne region, I don't think that four days will be sufficient. But maybe you have only one or two other things what you want to see in Paris itself. There are many great areas and hotels in Paris. Generally speaking see Saint German, Le Marais, the Latin Quarter neighborhoods suggested for first time visitors. And yes, the hotels are expensive and September is one of the busiest and this most expensive times of the year so be prepared to see high prices.
Champagne Region: As to seeing the champagne houses, it really depends on how many houses you want to see. I do not recommend driving from champagne house to champagne house unless you have a person who will skip the tastings. It is an easy train trip from Paris and takes about an hour to get to Reims or Epernay. Here is a thread in which people discussed choosing between the two towns: https://community.ricksteves.com/travel-forum/france/reims-or-epernay I've done trips to the Champagne region as day trips but I have a friend who has spend fours days in the region.
Versailles: It takes about 40 minutes to get to Versailles from Paris and most people I know stay about 4 hours but it could easily be a full day.

As noted on your other post, spend a bit of time searching the forum for ideas. https://community.ricksteves.com/travel-forum/england/flying-into-london-then-onto-paris

If you are doing two day trips from Paris, then 3-4 days is insufficient in my opinion. It also depends on how much time total you have available for the trip - how you divide between London/Paris/outside Paris is highly dependent on your interests, but if you only have a week then you'll have to do some significant prioritizing.

As noted above, if you are contemplating 2 day trips while in France, then 3-4 days is completely inadequate. Indeed 4 days without day trips would be insufficient for many. Especially for a first visit. As recommended in your other thread, get some guidebooks and watch a few videos to see what sites and activities most interest you. Use the search feature for accommodation recommendations.

Whether visiting Reims/Eperney as a day trip or as an overnight, dont even think of renting a car unless you have a designated driver who wont be drinking. Versailles will take at the very least half a day (about 6 hours from leaving your hotel until you return), and most likely more.

You can take the Eurostar (not the chunnel) from London to Paris. The tube is only for local transit in the London area.

You are trying to do too much in too little time.

For a first time trip to Paris, 3 days will barely scratch the surface without leaving the city limits.

Best places to stay? There are over a thousand hotels in Paris in all price ranges from bare bones to ultra luxe. What does best mean to you?

Stop by your local library or bookstore and pick up a book or 3. Maybe the Rick Steves' Paris or Fodors or Lonely Planet or ... This will give you a feel of what there is to do and how to do it.

I'll ask the same thing I posted on your London thread....how many days total do you have?

To many of us 3-4 days in either city is not adequate. Whoever told you that, or wherever you read that 3-4 days are sufficient for either London or Paris probably is not someone who likes to research to find out what is available to see.

Just as a for instance....I'm going to Paris this spring. I'm spending 21 days just in Paris AND I have not gotten to everything on my to-do iist. Now, I'll admit that my visits are museum-heavy but there is still a lot to do that is not art museums or churches.

Editing to add: It might be interesting for you to take a look at the Rick Steves itineraries for his "7 Day" tours for London and Paris. I have that in quotes because the way tour companies count days is to count your arrival and departure days so really it's only 5 full days for either itinerary. Both of these tours are good but literally just scratch the surface of what there is to see.

https://www.ricksteves.com/tours/france/paris
https://www.ricksteves.com/tours/england/london

Just to add to the previous post, indeed, I spent 10 days in Paris in 2021 and STILL didn't get to see everything I wanted to see. Mind you, my idea of seeing Paris was to see maybe 1-2 sites per day max, and spend the rest of my time just being a flaneur.

I spent 11 nights in Paris on my first visit last April and then 3 nights in October finishing up a trip that was focusing on the Normandy region primarily. I don't know who told you 3-4 days is sufficient or what your priorities are, though.

I'm spending 8 nights in London for my first London trip. (then 4 more in Paris and it still feels tight).

Yes Versailles will take realistically all day. We spent the day and then were exhausted but managed to go out for dinner afterward. And that was it , even being probably high stamina travelers.

It's not really a cheap place to spend the night but neither is London, from what I've looked at.