Best way from Lake Orta to Paris

There are no trains or buses from Lake Orta. You will need to take a taxi to another point (best is probably Milan) and then take train or plane. Your tour guide will help make the arrangements for you, but know that it is not cheap. If memory serves, it was nearly 100 Euros for me and my husband to get to Milan. It will be cheaper if you share the cab.

I haven't verified the information, but Rome2Rio.com is indicating that there is both rail and bus service from Pettenasco to Milan (via and/or changing in Novara). Service may not be rapid or frequent, but it would be much less expensive than a taxi.

This doesn't directly answer your question, but have you seen the Planning Tips section of your tour website? It has some details about getting from Orta to onward destinations in Italy: https://www.ricksteves.com/tours/italy/village-italy

In trip reports, I've seen people post here that since most people are heading to the same few places after this tour, the tourguide will arrange groups to share taxis and split the cost.

To get an idea of train routes, it's probably easiest to use Trainline (formerly Captain Train): https://www.trainline.eu/. They sell tickets for both Trenitalia and SNCF (French rail). It looks like a direct (no changes) train leaves from Milano Porta Garibaldi Station, while trains with one change leave from Milano Centrale. The trip takes 7.5-8.5 hours. Note that trains after mid-December aren't yet fully loaded into the system, so look for a few weeks out, just to see the options; the exact times may change, but the basic options probably won't. Use Milano as your departure point and Paris as your arrival point, without specifying stations, to find all routes.

To find flights, use Skyscanner: https://www.skyscanner.com/. Be sure to look for departures from Malpensa (MXP), since the Rick Steves link above says that's much closer to Orta than Linate airport (LIN), and arrivals into Orly (ORY) or Charles de Gaulle (CDG). Be careful of arrivals at Beauvais (BVA) - it's much farther from central Paris than the other two.

It's too early to book either trains or flights for September 2017, but it's not too soon to decide what you want. Airline booking opens something like 330 days before a flight, and the cheapest tickets go fast. Similarly, if you book your train when it goes on sale, which is 90 or 120 days before (I forget which), you'll be most likely to snag the significant discounts compared with last minute tickets.

There is indeed a train station in Orta San Giulio. I took the train from there to Milano Centrale this summer, with one change in Novara. It runs very frequently mornings and evenings (rush hour), less frequently during the middle of the day. It is easy walking distance from anywhere in Orta San Giulio, or you can take the little tourist train to the station, However, there is no ticket window or ticket kiosk, so buy your ticket in advance either online or en route when you pass near a train station.

There is also bus service from a few places on the lake directly to the airport (MXP), as I looked up the schedules for that too before my trip. It takes two hours though, as it's not very direct. A better choice would be to take the train from Orta-Miasino to Novara and pick up the bus to the airport there, as it's much faster.

You may have already checked, but the fastest connections from Orta to Paris are 10 hours. It's a beautiful ride but you may not want to spend a whole day that way. Maybe you want to stay overnight somewhere en route and really enjoy the trip, which would be my preference, but maybe you just want to get to Paris. In that case, I'd take the bus or share a taxi to Malpensa and fly. If you have to go to Linate airport (for more cheap airline options), the equation changes again, as it takes a long time and is somewhat inconvenient to get from Orta to Linate. Malpensa is 50-ish minutes from Orta by taxi.

I understand from this forum that the guides on this tour always help people sort out their onward travel, but that's a bit late to buy cheap airfare. In summary, I think once you decide how urgently you want to get to Paris, the transportation options will not be hard to sort out.