I have a visa for France only and not a Schengen visa. Can I travel from EuroAirport Basel Mulhouse Freiburg to my country?
Unless you have some very specific document like a limited territorial validity Schengen visa, a récépissé for an asylum application or a temporary visa delivered to let you leave the country after receiving an obligation de quitter le territoire français, chances are you have the right to transit in another Schengen country with your French visa (it's the case for most long-stay visas – work, student, family… – for example). But in any case Basel EuroAirport is entirely on French territory so you should not worry.
In practice, half of the terminal building is designated as the “Swiss part” of the airport with a special road and parking area to reach it from Switzerland without having to complete customs formalities for France but it should not impact you, you can use the French/German/EU half to enter the airport, check in, etc. and proceed to the international transit area like you would in any other French airport.
One thing you cannot do however if you want to avoid setting foot on Swiss territory is take the train to Basel and the bus to the airport from there (if memory serves, public transport connections are better from the Swiss side than from Mulhouse or Saint-Louis or wherever it is you can find a bus to the airport in France).