Paris in October

You could spend a month in Paris and not see everything, but that probably won't work for you, lol. A week is a good start. Add a day for Disneyland. Normandy beaches (I'm assuming you mean the D Day beaches) really requires at least an overnight stay in either Bayeux or Caen.

Get a good guidebook and decide which attractions you really want to see in Paris. Figure on 2-4 Attractions per day (allowing for travel times, meals, and maybe some relaxing strolls). Add them up, and you've got a fair estimate of how many days you'll need. Then start paring down to a reasonable number.

Unless you're driving from London (NOT recommended), you won't be using the Chunnel. You'll be taking the Eurostar train from St. Pancras in London to Gare du Nord in Paris. From there you'll want to take the metro or a taxi to your hotel to offload your bags.

Become familiar with the metro system. A good guidebook will help. As will the Paris transportation website : https://www.ratp.fr/en/itineraires

This itinerary planner is great for helping you get from place to place.

For starters , buy the current Rick Steves guidebook , and begin there .

Your question is too vague to really know how to answer appropriately. We were in Paris for 5 days in Oct 2017, our 4th time, and still didn't see everything we wanted to. If you can stay a week or a month there is plenty to do. The minimum for just Paris for a first time ideally would be a week. I suggest you get a RS book and decide what interests you most. And get the museum pass for sure no matter how long you are able to stay. I will say this, it was beautiful there in the fall.

Yes, you can use Uber in Paris. We have had good experiences with Uber there.
You should definitely familiarize yourself with the Metro.

We are planning to arrive in London for a few days and take the Chunnel to Paris. Any tips on taking the Chunnel, how far is the station from the Champs Elysees.

You can't take the chunnel (1) because it is the Channel Tunnel, not the chunnel, and (2) tunnels can't move!
You need to take a Eurostar train which runs from London St Pancras station to Paris Gare du Nord via the Channel Tunnel, roughly 1 train ever hour, and it takes just under 2½ hours.
The current timetable is here: https://content-static.eurostar.com/documents/UK_timetable.pdf
You can buy tickets on their website here: https://www.eurostar.com
See this video to see what it is like: https://www.youtube.com/watch?v=l5RAYy9Uymc

Tickets are on sale ~6 months in advance, and the earlier you buy the cheaper they are. Note you must be at St Pancras and through the ticket barrier at least 30 minutes before departure, because you go through both UK and French passport control before boarding the train.

Both St Pancras station and Gare du Nord are on the respective tube/métro networks, with which you will have to get familiar if you are staying in London or Paris.

By far the best way to see the D-Day sites is to take a one-day van tour of the area. You'll have a well-informed driver-guide and will be able to cover far more than you could manage on your own, even if you rented a car. A lot of the tours depart from Bayeux. You need to book them ahead of time. It's possible that they don't run every day in October; I'm not sure. Two companies often mentioned on this forum are Overlord Tours and Dale Booth. The (US-focused) Overlord tour I took in 2017 cost about 100 euros.

It would be great to have two nights in Bayeux, because there are other things to do there in addition to the tour: Bayeux tapestry, cathedral, pretty historic center, and a quite good WW II museum on the edge of town. You could manage to do the tour and see a bit of the town with just one night away from Paris by taking the train up to Bayeux sometime the day before your tour, then taking the train back to Paris late on the day of the tour. Check rail schedules and fares on the SNCF website. They only have information loaded for travel through May 18 at the moment. The train fare will be a lot lower if you are able to firm up your schedule and buy the round-trip ticket shortly after tickets become available. Buying at the last minute can be very costly. Take a look at fares for tomorrow to see what I mean. I see a range from 15 to 60 euros one way.

I'd suggest a week or so in Paris, plus two nights in Bayeux with a D-Day beach tour on the day between, as recommended above. Disney would be a separate day trip from Paris, in the opposite direction.

If time allows, give yourself two weeks in Paris and, besides Bayeux and Disney, take some day trips to places like Versailles, Chartres, Fontainebleau, Giverny, maybe Reims. See the "Explore Europe" link on this website for ideas about places to see in Paris and possible timelines.

Sorry; I meant to include a link to the SNCF website.

I like Barbra's math! ;)

I like Barbra's colloquialisms!

The Gare du Nord, where the Eurostar arrives, isn't particularly near the Champs-Elysées. But then again, Paris isn't SO big that it's extremely far away. It depends what your perspective is, so I don't really know how to answer your question.

We took the Eurostar from London to Paris. It was easy and pleasant. You leave mid-afternoon and arrive early evening. There’s an hour time change on the trip. Regular class is plenty comfortable and significantly cheaper.

We took a cab from the station. The problem is so did the rest of the passengers! It took 45 minutes in the queue. If we had taken the metro, we would have arrived at our B&B in 20 minutes.

How much time do you have? I’d do a minimum of five days for Paris alone, adding one day for each day trip. Your time there is precious, I can’t imagine wasting a day standing in lines at an American theme park.

We were in Paris last October. It is a wonderful time of the year. the crowds are smaller and the weather was wonderful. The leaves are changing and gorgeous. We walked a lot and rode the metro all over. Download the metro app, it was very helpful. You can put in your destination and it will show you the entire route including train changes, which are easy.

To plan your trips in and around Paris, here is the rapid transit interactive site: https://www.ratp.fr/en

The Champs Elysees is famous, but inconvenient as an anchor for planning.

Chunnel, Eurostar, it is still the same hole in the ground. Eurostar runs the trains. Buy your tickets as far in advance as possible to save money. Its website describes the London departure station, St-Pancras, in detail, including the procedure for going through French border security before departure. https://www.eurostar.com/us-en

Yes, take a full-day guided tour of the Normandy beaches. Excellent value for (substantial) money. Caen is another convenient base, bigger and with more choice of hotels and dining. Its well-reviewed "peace" museum also runs tours if you don't want to do the easy commute to Bayeux. Bonus: The fortress castle of William the Conqueror sits in the centre of Caen.