Hi Nandita -
Congratulations on your marriage!
First off, three places are too many in 7-10 days, especially if you're including travel time to-and-from India. Or did you mean just travel time between these three locations? No matter: still too many, and you'd have very little "relaxing and visiting" time. Are you planning on seeing family during this trip?
At most I'd only do London and Paris, and 10 days (10 nights) is much better than 7: you can easily spend a week in either and not see everything. If you are not counting your travel time to-and-from India, this would give you roughly 4.5 days in each:
Arrive in London on Day 1: figure on 1/2 day dealing with the airport, getting into the city, getting settled
Day 2 to day 5 in London
Day 6: take the train to Paris. figure on a little more than 1/2 day travel, getting settled.
Day 7 - 10 in Paris.
Fly home from Paris
We enjoy traveling in the fall when the summer crowds have thinned just a little but late spring can be very nice as well.
For where to stay and what to see in each city, the best start is to get yourself a good guidebook or two. Your interests, budget and accommodation preferences may not be the same as someone else's so the books will help you decide what's best for you. Additionally, you will find help on this forum once you've narrowed your choices at little.
It's very possible to plan your entire trip yourself but it takes time and energy. Some of us enjoy making our own plan and traveling independently (I do) but others prefer to the company of a group and tours which arrange a lot of the details for them. A good travel agent will also be able to work up an independent plan for you but I'd be cautious there: some agents are better than others. But whichever method you decide to take, there's no right or wrong way as long as it works for you.
Rick Steves - the website you've just joined - publishes printed travel guides AND offers group tours, should you be interested? You may explore tour itineraries, prices and dates here:
https://www.ricksteves.com/tours
And here is the online shop for guidebooks:
http://travelstore.ricksteves.com/catalog/index.cfm?fuseaction=catalog&parent_id=10
There are too many other types of tours offered by too many other companies to list so it's impossible to give you an average price: they can range from very expensive, custom-arranged luxury plans to budget-level, large-group escorted tours. I might suggest deciding whether to go solo or with a tour FIRST plus how much you'll have to spend as it'll help you narrow the scope of your options.
So, I hope this gives you some good ideas on how to begin!