There would be a lot of ripple effects. I'm more familiar with French history than English, so I'll focus on their end:
Given how long and grueling that siege was, it probably would have ended the war regardless of its outcome. An English/Huguenot victory likely means a peace settlement in their favor. But I suspect that this settlement would not last very long, and that the crown would eventually fight them again and defeat them. This might lead to a harsher settlement than that of 1629 (which eliminated their political/military privileges but upheld their religious freedoms from the Edict of Nantes).
If a renewed religious war takes place in the 1630s, then France is not likely to get involved in the Thirty Years' War, at least not until its own domestic conflict is resolved. That could mean that the peace settlement of 1635 holds, or perhaps that the Catholic side in the war presses its advantage against the weakened Protestant side (with Gustavus Adolphus having died).
Overseas, the struggling colony of New France was captured by a English force in 1629, but this was after the war had ended IOTL, and it was returned to France. With an outright English/Protestant victory it perhaps wouldn't be returned at all - or perhaps France would receive it back on the condition that Protestants could continue to settle there (that right was taken away during the 1620s). Either way North American history would be very different.