  We prove that the free Fock space ${\F}(\R^+;\C)$, which is very commonly
used in Free Probability Theory, is the continuous free product of copies of
the space $\C^2$. We describe an explicit embedding and approximation of this
continuous free product structure by means of a discrete-time approximation:
the free toy Fock space, a countable free product of copies of $\C^2$. We show
that the basic creation, annihilation and gauge operators of the free Fock
space are also limits of elementary operators on the free toy Fock space. When
applying these constructions and results to the probabilistic interpretations
of these spaces, we recover some discrete approximations of the semi-circular
Brownian motion and of the free Poisson process. All these results are also
extended to the higher multiplicity case, that is, ${\F}(\R^+;\C^N)$ is the
continuous free product of copies of the space $\C^{N+1}$.
