The Euroairport in Mulhouse connects Basel with most of the European and North African Cities. The two main-stations allow traveling by train to Basel from France (SNCF) and Germany (DB) and certainly any place in Switzerland (SBB.) For international traveling Zurich international Airport it is only about one hour by train to Basel. Basel itself has an elaborated bus- and tram-network (BVB.) which is very useful for daily journeys.
here are some useful maps: