It may sound weird at the beginning to think of a prince wanting to became a member of a parliament of a republic. But if you think twice, it's not necessarily a contradition:
the parliament is a symbol of DEMOCRACY, which, despite what some republicans think (I know plenty of them) is not the same thing as REPUBLIC and is not a contrary concept of monarchy. I know, I know, it's the parliament of a republic but it represents democracy, people's right to choose the destiny of their country. The Republic's main symbol is the head-of-state, the president. the main (not the only one) difference between monarchy and republic is in the choice (or lack of it) of the head-of-state. Charles-Philippe is not running for president...He doesn't not aim to represent the republic but to represent the people and democracy
It's also quite common to see in some republican countries some people feeling surprised about monarchists (in general not just princes) participating in the political life of the republic. Again they misunderstood democracy with republic, but also keep forgetting that it's not because I don't like the way the country works that I don't have the right to participate in the decisions of my country. Charles-Philippe may prefer that France was a monarchy but french people don't. He has to respect that but that doesn't mean that he shouldn't participate in french political life. It's a move on decision and as jonc93 said findind new ways of helping the people.