Flights to/within Europe

How long before to arrive at airport - Depends on the airline. They should be telling you on their website.
For economy airlines, you have to be at the gate a certain time before the flight departs, or you will not be let on the plane, typically 30 minutes. And, sometimes (Easyjet) they do not open the check-in desk more than 2 hours before departure.
Read very carefully the check in rules. You usually check in online, up to a month in advance. And some airlines (Ryanair) charge you extra if you haven't printed your own boarding card.
Full service airlines are usually more flexible.

• Train London Paris. The UK is not in Schengen, so there is passport checks. Both UK exit and France/Schengen entry take place at London St. Pancras station before you get on the train. Therefore you must be through the ticket barrier at least 30 minutes before departure.
• Fly Paris Florence. No passport checks (intra-Schengen), but you will need your passport as ID.
• Flight Rome to Zurich. Ditto. Switzerland is not in the EU, but it is in the Schengen Area.
• Flight Geneva back to London. Yes, passports as you are exiting Schengen and entering the UK.

Technically there is customs in and out of Switzerland, as it is not in the EU, but it is never an issue, just walk through the "nothing to declare" door.

2 of the flights are Veuling and 1 is Swiss Air. I will check their websites. Thanks! But I'm still looking for a better estimate. I am trying to plan what times to actually plan transportation. For example, if it takes an hour (less, being conservative) to get to Orly from our hotel, and we have a 9am flight to Florence, do we need to leave hotel at 5am? 6am? 7am? That one in particular is a Sunday morning if that makes a difference.

Like Chris said, check your budget airlines time requirements carefully. Two of your airports are big and security can take awhile so I'd map backwards and allow a full 2 hours AT the airport (CDG and FCO). Geneva is smaller but I haven't flown from there in several years so I can't comment on that airport nor travel time to get to the airport. Last summer we had an early Sunday morning flight from FCO to Toulouse. Our driver, arranged through the hotel, picked us up about 45 min before our desired 2 hour time to be AT the airport. There wasn't much traffic and we zipped there in about 40 minutes.

EDIT: we were flying Alitalia not a budget airline from Rome to Toulouse.

As far as your train from London to Paris, I know the website says 30 minutes before but based on personal experience, a one hour arrival time for the Eurostar is a more comfortable cushion.

Check your airlines' websites. Are you checking luggage? That takes time in addition to line ups at security. And then a possible long walk to your gate. All these are busy airports even first thing in the morning so I would say at least 2 hours prior to departure. I'd rather a gentle stroll to the gate than running to make the flight.

Ideally, no checked luggage. I purchased backpack luggage that I think is going to work, but might end up having to check.

There are so many variables--time of day, checking luggage, checking in online or not, etc.

My standard is arriving at the airport two hours ahead of a flight, i always try to check in online and print my boarding passes before I get to the airport. If Ihave to check luggage I still try to check in online so I just have to go to "bag drop."

When you arrive in London the first time you will have immigration and customs. You will go through Schengen/French immigration in London before getting on the train. You will go through Schengen exit immigration in Geneva and immigration again in London.

There is no immigration check between Schengen countries but the UK is not part of Schengen. There are no customs checks between EU countries. If offered you walk through the blue door "EU Arrivals" every time except after your flight from the U.S.

7-9 am is prime time for businees flyers so the airports will be busy including security. There will also be traffic on the road and crowded public transit.

Don't try to cut it too close.

For flights out of Swiss, I allow two hours at the airport if it's early in the week and a little more if it's a Friday or the weekend. There is enhanced screening and security now and the passport check lines and the time it takes to get through them has increased.

You are asking for a precise answer when there is no precise answer. For all domestic flights in Europe, regardless of airport, we plan to be at the airport two hours in advance and absolutely at the airport an hour and a half. If you have you boarding pass and not checking luggage you might shave it to an hour and fifteen but absolutely no less.