For the English, there are a few of them, but the main one I can think of is that the Kings use the New World Colonies to raise money independently of Parliament, effectively taking away the primary power that Parliament has over the Monarchy. Though, the English Civil War MUST be avoided, otherwise it doesn't matter.
For the French, it's depressingly simple. The French could easily get themselves into a ton of debt after a disastrous war with Spain, the HRE, or both at once. The debt is so extreme that whatever King is in charge at the time is forced to call the estates-general. However, maybe civil unrest happens, maybe it's before the TYW and the Huguenots problem is not solved yet, nothing is able to get done, and they have to keep calling the estates-general year after year until it just becomes customary to call them and keep them in session the year over. Then you just need a stand-off between the two of them to end like the English Civil War, and you have a Parliamentary France and an England with a powerful King that could easily turn absolutist given the right monarchs.