To pick up your last point first: yes, of course you can do this trip on your own. The places you mention are some of the world’s most popular tourist destinations and thus are highly developed in terms of visitor infrastructure and options. I prefer independent travel—it’s more flexible, travel planning and research can be fun, and there’s the joy of making your own discoveries. But there’s the usual problems, too, the biggest being the amount of time required to do this. That said, if by ‘taking the help of a travel agent’, all you mean is using one to make travel and hotel bookings, that’s probably sensible. Do your research and list your preferences to an agent. I can’t possibly help with an itinerary, since I am not aware of your preferences (what in Switzerland interests you, for instanc—cities, nature, culture…). Do spend time on myswitzerland.com, italia.it/en/home.html and in.france.fr—all official tourism websites—and make a shortlist of options.
One suggestion I can offer are on wine and cheese tours in France. There are several wine tours on offer; see burgundyonaplate.com, which offers a range of tours including one-day tours in wine-growing regions. If the travel seems too complicated, take in a wine and cheese lunch in Paris with O Chateau (€75; o-chateau.com); they also conduct day tours to Champagne (€245). Or consider Wendy Lyn’s ‘Taste of Paris’ tour (€160; wendylyn.paris/food-winetours/paris-food-tour).
As far as visas go, a Schengen visa will give you entry to all three countries. Remember that you should apply for the visa at the mission of the country that you intend to arrive in. Intra-country transport: Western Europe is, obviously, a small subset of a small continent. Trains are a good option, scenic and efficient, with many cities connected on the Rail Europe network (raileurope.com). If you’re travelling around Switzerland, get a Swiss Travel System ticket, which applies to travel on train, bus and boat around the country (swisstravelsystem.com).