Wasn’t the last king Carlos? Thats why Ignes refer to the baby as Carlo-zen because she refer to the previous king as “prince Carlos” and feels uncomfortable calling someone else prince carlos. She was his maid before being king so thats why he still thinks of him as prince Carlos.
He wasn't King yet, otherwise they wouldn't be calling him "Prince". He was the heir to the throne and Aura's brother (I think), but he was never officially coronated before he was killed.
Actually, a short story in one of the manga volumes reveals that Ignes (I think 7C's calls her Ines) was Prince Carlos' LOVER. (I think it was the volume where Carlos was born.)
While he never married (because he was infertile), his relationship with Ignes was such a well-known "secret" that Aura has to be stopped by Ignes herself from saying that she considers Ignes her AUNT when Carlos is born. This happens when Aura asks Ignes for permission to call the child Carlos (literally minutes after the birth). Aura says that child was only born because Prince Carlos did all of the legwork to create the world-hopping spell, but died before he could see it in use. While Aura wants to name the child in his honor, she wasn't sure if that name would cause Ignes emotional pain. The text implies that both Carlos and Ignes considered each other the love of their life (and that neither had other lovers and desperately wanted to have a child together) and that Ignes was devastated when Carlos died to the point that Aura views Ignes as Carlos' de-facto widow.
During the whole conversation, Ignes' main concern is Aura's position, mostly being more concerned about what it would do to Aura's reputation if the Capuan nobility found out that the QUEEN was asking permission of a MAID. While she does seem a little bit pained at the suggested name, she says she will be fine, justifying it as the closest thing to Prince Carlos having children.
So, the reason she refers to child Carlos as "Carlos-zen" is because calling him "Prince Carlos" makes her remember what she has lost. She will ONLY do so if she needs to refer to him in public where calling him anything other than "Prince Carlos" could ruffle some feathers.
As a side note in retrospect, that short story makes it pretty obvious why Aura always sends Ignes when Zenjirou needs to go somewhere for a longer period of time--Ignes has her absolute trust. The nobles of Capua KNOW that Ignes CANNOT be swayed--she cannot be swayed with political schemes or woo'd with marriage proposals like some of the other maids. (And her unending love for Prince Carlos would prevent her from EVER making a pass at Zenjirou under any circumstances.) Her loyalty to the royal family is ABSOLUTE because she is an unofficial member of the family.
Wow, this ended up as a bigger wall of text than I expected... Wait, do I need to mark this as a spoiler since it technically hasn't been revealed in the manga? Frankly, I'm not sure if it will EVER be discussed there due to the "taboo" nature and its inclusion in the volume extras.
*edit: Another nugget I remembered--Prince Carlos died of natural causes, not murder or war. From what I remember, it's not specified EXACTLY what caused it, but it was implied to either be A) the condition that left him infertile causing him to die young or B) he overworked himself when creating the world-hopping spell.