Let's say the genders, personality AND health of Charles de Valois, Duc d'Angouleme and of Marie Elisabeth de France are reversed.
So by the time of death of Charles IX in 1574 he has a 2-years legitimate son and a rather obscure illegitimate daughter.
In OTL the Duc d'Angouleme lived till 1650. So the reign of TTL Charles X will be pretty long (1575-1650). And with his interesting personality...it will be fulfilling.
https://en.wikipedia.org/wiki/Charles_de_Valois,_Duke_of_Angoulême
The obvious results is that OTL Henri III may stay the King of Poland, and OTL Henri IV may stay the King of Navarre.
Catherine de Medici will likely become the regent for her infant grandson, though Elisabeth of Austria (never to return to Austria TTL) is a likely contender, so we'll see a tug-of-war between Queen-Mother and Queen-Grandmother.
And Marie de Medici may still happen TTL as Queen of France - she's 3 years younger that TTL Charles X. Other than her, marriage alliance with Lorraine may be suggested, but the likely bride, first cousin of TTL Charles X, Elisabeth of Lorraine, OTL Duchess of Bavaria, is sterile.
I'd say the childhood of this boy will have a LOT in common with the childhood of Louis XIV - a child king on the throne of the country during the civil war.
While the idea of a surviving Valois France is interesting I think you might be quite a bit off about the situation within France. The Crown's authority had began to rapidly decline thanks to the constant civil wars. Looking at the era, both the Catholic League and the Huguenots were fairly evenly matched. Not in terms of direct manpower obviously (Catholics made up at least 80 % of the French population, probably closer to 90%) but in terms of armies fielded and influence. It wasn't until Henri III had the Duc de Guise and Cardinal de Lorraine murdered and was then himself assassinated, that things changed. The Catholic league was basically headless, while the forces of the Crown were combined with the full forces of the Huguenots. And even then it still took what, five or six years and a conversion for Henri IV to emerge victorious.
The main issue here is the Valois religious policy. Its moderation meant that the Crown was alienated from both the Catholic League of the Guise and the Huguenot forces. This would be after the St. Bartholomew's day massacre, so no chance of real Protestant support for the crown. The Valois' best bet would be to fully endorse the Catholic League, end moderation and go into full scale war. It would be bloody, long and devastating, but it would ultimately get results. Destroy the Huguenots ability to wage war completely. It was already crippled after the massacre, so the late 1570s and early 1580s would be the best time to finish them off, before they regrouped and continued the wars of religion for nearly 20 years.
I imagine the war could end with a modified version of the Edict of Nantes, allowing religious toleration but curtailing political and military freedoms. Of course, after ending the Huguenot threat the Guises still need to be neutralized. Maybe the Guises attempt to seize the young King and take control of the government and fail, leading to their fall. Or something similar. But either way the internal threats need to be removed in order for France to prosper.
Also, the tug of war over the regency would be multiple, as many would have a claim to a long-term regency. The Duc d'Alençon, as the King's uncle, would have a very strong claim, followed by the Queen Mother Elisabeth of Austria, the Queen Dowager Catherine de' Medici and King Henri of Navarre, as next in line after the Valois. So that in itself is also a potential civil war. Someone, probably Catherine, would need to take charge quickly and remove the other rivals politically.
But, if France can get its act together, then the Valois have a real potential to rival the House of Habsburg in terms of European domination. They would have France, the Polish-Lithuanian Commonwealth (assuming someone gives Henri de Valois a b*tch slap, makes him get his act together and embrace his new Kingdom) and potentially England. Remember Elizabeth I nearly married her "frog" Alençon, so there could be a potential marriage right there. Unlikely mind you, if the Valois go full Catholic on their Huguenots, but still possible. If Spain is able to really threaten England, then the Queen might turn towards a renewed France for friendship. Perhaps Mary, Queen of Scots escapes to the Spanish Netherlands and weds Juan de Austria, creating a Spanish menace to threaten Elizabeth.
Finally, as to marriages, that will entirely depend on the international situation. If the French-Habsburg rivalry heats back up then you can kiss an Infanta or Archduchess goodbye. France would probably turn to Italy for a bride. An interesting idea would be to have Duke Alfonso II of Ferrara have children with his second wife Barbara of Austria, with a daughter becoming Queen of France. Or have Henri and Margot have issue and have a Navarrese Princess bring some of her families vast holdings as a dowry to her cousin Charles. You could even still use TTL's Marie de' Medici, or Catherine de Lorraine, if she is less religious here. However, I will say a German match is very unlikely.
One other thing: at one point in 1580 Catherine de' Medici attempted to put forward a claim to the vacant throne of Portugal. I can't remember on whose behalf, but it could be very interesting later down the line. Maybe Charles X will decide he likes how his name sounds in Portuguese?
