To pick up your last point first: yes, of course you can do this trip on your
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).
cheese tour
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Rail Europe