HELP: Itenerary for Paris 04/10-4/17 and maybe one day in London.

There is more than enough to keep you happily busy in Paris for that length of time! On the question of it's worth going to London for a day.... that depends. If you don't believe you will ever return to Europe again and cannot imagine not seeing London, then by all means take the trip! Eurostar makes it an easy and painless trip and since it goes city center to city center it's not a terribly inefficient use of your time.
However, if you believe that you will be returning to Europe, then I would leave London for another trip. Like Paris, London has a multitude of wonderful things to see and do and would also keep you happily busy for at least a week!!

One of the joys of Paris is wandering the neighborhoods. Given you rather limited time, I'd suggest you do a walk with with Paris Walks or Discover Walks. They have a variety of walks (which you can google ahead of time and add to your list of activities). There is no need to make a reservation. Just show up at the appointed time at the appointed place. While it's certainly enjoyable to wander on one's own, it can be a bit frustrating so this gives you a way to see parts of Paris you might not come across on your own without feeling that you are wasting your time!
Other ideas - pick up picnic supplies and picnic in the Champ du Mars and watch the Eiffel Tower light up...

As for food...ah, where to begin! Definitely take in one the weekly markets - Bastille is a personal favorite but others are quite wonderful as well. If working around specific days/times is problematic a stroll down Rue Montorgueill, or Place d' Aligre (which has a market 6 days a week) is a tasty and worthwhile excursion.
As for restaurants... again where to begin. So I will suggest two sites that I have found to be reliable :

www.davidlebovitz.com - American pastry chef living in Paris. His recipes are excellent and his restaurant recommendations are spot on as well!
www.parisbymouth.com - I enjoy the writing and have also found the restaurant reviews/recommendations to be spot on.

Happy researching!!!

I would concur with previous remarks. There is plenty to do in Paris and one day is very limited for a London trip. If you do go, even though you will be paying a double night, I would recommend a night over in London just to offer you a little extra time.

That said, if you want to pack your trip in and are a monument lover, a day in London would be a great change of scene from Paris. Most of my favorite monuments and buildings are in London and though tours would pack an itinerary, being able to just see so many of them can be a great use of the day. Go slow in Paris and then have a packed day in London could be great.

If you go, make sure you are checking your prices daily. You should expect to pay $75-$85 at the cheapest rate during the week and I have found you can still get those rates 2 weeks out (but usually the further out the better). I recommend also checking the price using the voyages-sncf app (I usually spend less for same tickets here and you can just keep your QR coded ticket on the phone rather than printing-it stores within the app)

What do you want to see or do in London? What are the MUST for you in London?

There is already so much to see and do in Paris why go to London? It's your first trip to Europe. Believe that you will return.
Make London a separate trip later. Don't be over ambitious on your first trip - a typical mistake for first timers.
I have been to Paris 3 times and did not repeat any of the activities. I are still things on my wish list that would fill 2 more trips.
Just focus on enjoying Paris on this trip.

I agree that a day trip to London would be a bad use of your limited time. You could easily fill a week, or even two, just in Paris, and there are lots of great day trips to much closer places -- Giverny, Chartres, St-Denis, Reims come immediately to mind. Your "day" in London will be nonstop, you'll be rushing around a very spread-out city trying to see things and make the train back (must be there at least half an hour before departure, more if possible). I'd save London for another trip.

The "Explore Europe" link above will give you Rick Steves' best take on Paris sights and priorities, and I think most posters here would agree with them on the whole. Use a guidebook for additional information (maybe from your library if you don't want to invest in or carry one). Pick what places interest you most, find them on a map, and build days around locations. Try to see one "big" thing in the morning and have another one or two for the afternoon if there's time. If you group sights by geography you'll often be able to walk between them and take in the street life, stop in cafes, etc.

Have you ever been to London before? I have done the London to Paris day trip to get a taste and decide to see if I liked it enough to return.

It's very doable.