Can we break RSA with an optical Fourier Transform?
The horsepower underlying this algorithm is the Fourier transform


Not quite; the algorithm is to generate a superposition of states, compute the modular exponentiation of those states (generating the superposition of those results), and then use a Quantum FFT (actually, the inverse FFT[1]) to find a periodicity (and from such a period, you can deduce the factorization).

The issue for you is that this is an inherently quantum operation; the hardware you linked to performs a Discrete (Classical) FFT [2], which doesn't operation on superpositions.  And, if you don't perform the inverse FFT on a superposition, then you can't implement Shor's algorithm.

Hence, your idea using an optical hardware within superposition doesn't solve the problem at all...


  Are such alternatives viable (in a near future) to break RSA?


It doesn't appear that way...

[1] Requiring an inverse FFT isn't the main objection - I believe optics can perform that operation as well...

[2] Actually, it's rather easy to compute FFTs (and inverse FFTs) in software - the linked hardware's just claims it can compute it somewhat faster, but software already is pretty fast...