Can anyone recommend universities in France and Switzerland?

Why France and Switzerland? If you want to study in English, study in the English speaking world.

In France the public universities are required to teach all their undergraduate courses in French but you can attend a private university like the American University of Paris that will teach you in English (well sort of English).

Switzerland has some public university courses that are taught in English. They are mainly in Finance, Engineering and Computer science. You will be able to take some classes in Psychology in English at the University of Neuchâtel or Zurich but not an entire degree. Those are both decent universities, ten times better than the American University of Paris which is just for Eurotrash. Of course, you will have to have university level French or German.

Can't help with the second part of your question because I do not know what a 'varsities' is or the meaning of 'neighbourhood countries'. What language do you speak at home?

There aren't any. If you want to study in English, you need to study in an English-speaking country. Once you get your first degree and are looking for possible postgrad courses, then the options widen somewhat, but even then the vast majority of university courses are always going to be taught in the local language of the country in question.

But for what it's worth, here are the top French and Swiss universities for psychology, as ranked by the QS World University rankings (with approximate worldwide rank shown in brackets):

Geneva (51-100)

Zurich (51-100)

Aix-Marseille (151-200)

Paris Descartes (151-200)

Bern (151-200)

Lausanne (151-200)

As you can see, none of them are exactly world-leading...

If you want to study in English (& you meet standards for English language), then you need to go to school in an English-speaking country. France requires fluency in French. Switzerland has 4 official languages, and Swiss are generally fluent in 2-3 of them plus English. But school will be the language of that region of Switzerland, most commonly German (and it's Swiss-German at that!) or French.

So you must be fluent in the country's language, both to meet school requirements, and visa requirements.