Do you need an ESTA or a visa for your trip to the United States?

Hello, I am a Belgian citizen, I asked for an ESTA on September 6 which was granted to me without worries.But as I left for the 6 -month -old language studies I was told that you have to ask for an F1 visa that if not with the esta that I had to go out after 90 days.

I did all the registration procedure at school, payment of the SEVIS ... And the day of my interview yesterday PAF I am refused the visa supposedly that nothing proves that I will come back after my studies.

My question is the following is the ESTA which was granted to me with the refusal of the visa remains valid despite everything or I will not be able to travel with it?

Thanks in advance