The second charge/conviction would not be precluded, but the evidence that comes out could help the accused establish that the first was a wrongful conviction.
One could apply for review as a wrongful conviction
If the Crown introduces evidence at the second trial that clearly establishes innocence for the first conviction, there is path for review by the Minister of Justice as a wrongful conviction. The new evidence would very likely meet the threshold for being "new and significant" in that it was not before the court in the first trial and would have affected the verdict if it had been.
Autrefois convict does not apply
The second prosecution would only be precluded if the second charged offence was for the very same "delict."
For example, if A is involved in a scheme to get someone's money, and A is convicted of conspiracy to defraud, A could not be later (or at the same time even) be convicted of conspiracy to steal based on those very same acts.
However, the principle of autrefois convict does not prevent a charge or conviction of a completely different offence, with different elements or different facts. For example, if A was convicted of assaulting B, that does not preclude a later conviction for theft from B, even if that theft happened at the same time. Likewise, a conviction of an assault of B does not preclude a conviction of an assault of C.
These principles are explained in Kienapple v. R.,  1 S.C.R. 729.
Issue estoppel does not apply
Regarding the risk of inconsistent verdicts, there is a principle of issue estoppel in Canadian criminal law. If an issue was decided in the accused's favour in a first trial that resulted in acquittal, the Crown is forever bound to that fact. See R. v. Mahalingan, 2008 SCC 63:
 ... issues which were decided in the accused’s favour, whether on the basis of a positive factual finding or a reasonable doubt, are the subject of issue estoppel.
 It is thus not every factual issue in the trial resulting in an acquittal which results in an estoppel at a subsequent trial, but only those issues which were expressly resolved or, given how the case was argued, had to be resolved for there to be an acquittal. If a particular issue was decided in favour of the accused at a previous trial, even if the issue was decided on the basis of reasonable doubt, issue estoppel applies.
In the circumstance you describe, the accused was not acquitted in the first trial, so the form of issue estoppel developed so far in Canadian law would not be available.