Suppose that there is a continuous signal with highest frequency known.
Is there a way so that we only sample the signal finite times and obtain the Fourier transform of the original signal (which allows to obtain the original continuous signal by inverse Fourier transform), using the knowledge of highest frequency?
No, this is generally impossible unless the signal is periodic. A band-limited signal (and this is what you're referring to if I understand you correctly) always has infinite length, i.e. it cannot generally be represented by a finite number of samples.