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No, you are not right with your understanding that you need to enter and stay in the country of your first destination. You may enter the Schengen zone wherever you like to; lots of visitors especially to smaller Schengen countries enter the Schengen zone and go through immigration at the major European hubs and continue their travel on Schengen internal flights without any further immigration procedures. Once you have entered the Schengen zone you can proceed without further immigration crossing internal Schengen borders like between France and Switzerland.
You need however address the visa application to the country which is your main destination, or if your stay should be equally distributed, to the first country of entry. In other words if you apply for a visa at a Swiss Embassy you need to provide an itinerary which either has Switzerland as main destination or as the first country of entry.
Planning a tour through Switzerland you could easily stay at a hotel in Mulhouse for the first night before you continue your travel to other locations in Switzerland.
For hotel bookings you can easily check the country by the postal code in the address; French addresses show a five digit postal code starting with 68; Swiss addresses have 4 digits starting with 40; should the postal code be five digits and starts with 79 the hotel would be in Germany.
The borders between Switzerland and France are still manned, not by immigration officers but by customs officers since Switzerland is not a member of the European Economic Area (EEA) which forms a customs-free zone.