An atomic frequency standard based on a fountain of cold cesium atoms has been in operation in our laboratory for a few months. Ramsey fringes as narrow as 0.7 Hz have been obtained. The short-term frequency stability, measured against an H-maser, is 3 10(-13)tau(-1/2), probably limited by the local oscillator frequency noise. A preliminary evaluation of some systematic effects shows that cold collisions will be the limiting effect for long-term stability and accuracy. Measurements of this shift presented here, using a magnetooptical trap, show that at low density an uncertainty of about 10(15) is obtained. Under these conditions, the number of atoms is large enough to allow a potential stability of 10(-13) tau(-1/2) to be reached. When optical molasses is used, the initial density is lower and collisional effects are reduced by a factor of three.