I just moved to Basel 7 months pregnant. Ok the system is rather complicated because insurance is not provided through employment. For us we first lived with our in-laws near Zurich, but we knew we wanted to move to Basel. Here is where we had problems because you must be registered in the city in which you will live which requires a lease contract. We registered using dh's brother's address in Basel stadt, but ended up living in Basel city. I went a month without seeing a doctor. I am now at the university hospital here which is a teaching hospital so I will not have the same mid-wife or doctor. I am ok with that though as everyone is really nice at the hospital. Most everyone I have come into contact with spoke English so that should not be a problem.
When we first planned on moving here, I was determined to set up a relationship with a mid-wife and doctor. As things progressed, I just kinda let go and accepted that I would be taken care of and I felt much better. The hospitals here are very natural birth friendly and the care I have received has been excellent. Good Luck in beautiful Geneva! Dh's family is from that area and I love it there. Let me know if you have anymore questions.
Happily married Cajun transplanted to the Swiss hills.Mommy to two beautiful boys Louis Jean 03-07-07 and Elliot Millard 05-12-09