Foreign exchange is pretty much open during normal business hours and closes at the end of each day. Starts early morning Monday until Friday afternoon when major financial centers are closed for the day. However since another major financial hub somewhere across the globe should be operating by the end of normal business hours locally, transactions still keep flowing. Making it a 24 hour market as it follows day light across the globe.
Depending on where you are, Foreign exchange market has different market hours. For example, financial centers in Tokyo starts their early Monday operations while it is still Sunday night in New York. Therefore market hours in New York would be Sunday afternoon until Friday afternoon at New York close. While market hours in Japan starts Monday morning until early Saturday morning when it is still Friday afternoon in New York which is the last major financial center to close shops for the week.