If only the children of Frank and Helen could be the true kings and queens of Narnia, then the Pevensies could not be the true monarchs either. But they were. It doesn't matter whether or not Caspian is descended from Frank and Helen. What is important is he is descended from Adam and Eve. I believe it is Trufflehunter who says "Narnia was never right unless a Son of Adam was on the throne." Or something like that. Only Sons of Adam and Daughters of Eve can be kings and queens.
When Dr. Cornelius says that Caspian is the true king of Narnia, he is not only referring to Caspian being a human(a Son of Adam). He is also referring to Caspian being the rightful heir to the throne instead of his uncle. Caspian X is the eldest and only son of Caspian IX. By right of succession Caspian should be on the throne, not Miraz.

It does seem odd now that I think of it. However, Archenland and Narnia seem to have a strange relationship anyway. Narnia comes to help Archenland in HHB, but there is no indication that they ever aided Narnia. (For example when the Telmarines invaded Narnia). I think Aslan mentions something about Narnia being in disarray at the time of the Telmarine invasion. I always took that to mean that there wasn't a ruler at the time or that it wasn't a human.
After some more thought, it occurred to me that at the time PC was written, the Magician's Nephew had not been written yet. I'm assuming this means that Lewis had not yet come up with Frank and Helen. If Lewis didn't know about the original king and queen, it would be almost impossible for the Narnians to. (I wonder what the books would have been like if Lewis had had a chance to go through and fix the discrepancies).
I agree with what daughter of the King said. Also, a Telmarine would work a lot better than an Archenlander. The Telmarines who are in Narnia would be much more likely to accept Caspian as their king than some stranger who conquered them.

It does seem odd now that I think of it. However, Archenland and Narnia seem to have a strange relationship anyway. Narnia comes to help Archenland in HHB, but there is no indication that they ever aided Narnia. (For example when the Telmarines invaded Narnia).

Acully,in HHB,Narnia was protecting their own interests. Susan kinda helped start the war,and they knew that if Anvard fell,Cair Paravel would be next. Also,somewhere in the LB,Tirian mentions that he could run away to Archenland and get troops there.

I did think that myself,that when the Four Sovereigns left Narnia,that Cor and his decedents would have the right to Narnia's throne,being heirs of Frank and Helen.

Interesting points!

Why would Dr. Cornelius say that Caspian is the true king of Narnia if he is an old Narnian? I would think that he would want a descendant of Helen and Frank to be the king of Narnia. I wonder that no one else in the books tried to get to Archenland to get a descendant to reign over Narnia.

Well, would that be right, for instance, for the Archenland king to rule both Narnia and Archenland? Maybe I don't know much about dynasties and heritages, but can one king rule two countries without merging them--and would that be right?

I didn't mean that the Archenland king would rule both countries. I meant that a relative of that king (a sibling or cousin perhaps) would be king of Narnia.

Well, would that be right, for instance, for the Archenland king to rule both Narnia and Archenland? Maybe I don't know much about dynasties and heritages, but can one king rule two countries without merging them--and would that be right?

Yes! The King of Sweden ruled both Norway and Sweden from 1814 until 1905, and the two countries were not merged.

The Danish kings had ruled Norway for about four hundred years before that, and some Danish kings indeed tried to merge the two countries, but it somehow never really worked. In 1814 they were told to give up Norway and hand it over to Sweden because of the wars against Napoleon, and the Norwegians tried to become independent and wrote a Constitution. We didn't get full independency, but the Constitution contributed to us not being merged.

In 1905 Norway broke away and got its own king again, like we used to have before the fourteenth century. His grandson is our current king

So maybe the King of Archenland could rule both countries until such a time that Narnia was able to find a new king and reestablish the kingdom.

However, Archenland and Narnia seem to have a strange relationship anyway. Narnia comes to help Archenland in HHB, but there is no indication that they ever aided Narnia. (For example when the Telmarines invaded Narnia). I think Aslan mentions something about Narnia being in disarray at the time of the Telmarine invasion.

When he helped Caspian escape from Miraz’s castle, Doctor Cornelius tells him to flee the court of King Nain of Archenland. He said King Nain would be good to Caspian. So I would say Archenland was still on good terms with Narnia, or at least Old Narnia, at that time.

Can I suggest a plausible, but not probable, idea?

We know that there were humans in Narnia besides the Pevensies (such as Sir Peridan). It's possible that some of those human Narnians were in charge after the Pevensies left. Maybe they were corrupt, maybe there was a civil war, or maybe something else caused disarray when the Telmarines invaded. It's also very common for the conquering people to take the women of a conquered nation as wives, particularly the ranking women.

I'm just saying, we know nothing about Caspian's mother, save that she was the only Telmarine who was kind to Cornelius. Isn't it possible she was descended from human Narnians who were captives of the Telmarines? Maybe even raised on the old stories, told through the ages from her ancestors.

Hey, it's possible. Not probable, but possible.

(More than likely, it was more the idea of Caspian being a Son of Adam who followed Aslan than anything else. But still.)

I'm just saying, we know nothing about Caspian's mother, save that she was the only Telmarine who was kind to Cornelius. Isn't it possible she was descended from human Narnians who were captives of the Telmarines? Maybe even raised on the old stories, told through the ages from her ancestors.

Dr. Cornelius does say that Caspian's mother was the only Telmarine who was ever kind to him. And Caspian had a nurse with Dwarf blood in her. I've always wondered just based on those two things who Caspian's mother was and if she ever had any contact with the old Narnians.

Good topic!
I also always wondered about this. There was another point where there was no ruler in Narnia and their kin in Archenland did not step in to take the throne;

Before the Pevensies came - did the White Witch defeat and kill whatever king / queen was ruling at the time or was there noone ruling so that she just conquered Narnia which had no ruler at the time. If so what did happen to Frank and Helen's line and if the line continued in Archenland - why were the Narnians so shocked to see humans, after all it's less than a days ride away! Maybe the winter cut off the pass

Well, honestly, part of the problem is that Lewis never intended to write more after LWW, so he hadn't even conceived of King Frank and Queen Helen, or Archenland, or anything when he wrote LWW. I believe I heard somewhere that Lewis intended to go back and rewrite LWW to fit in better with the rest of the series (don't know if this is true or not).

I believe he was intending to rewrite the entire series, Lirenel. But he died before he could. Now we'll never know what he would have done with them.

Wow. That's really interesting. I never knew that Lewis intended to rewrite the books. That'd be a really interesting thread. 'What would CS Lewis have changed if he re wrote the books?' What inconsistencies would he have fixed? Would he have put in any new things? Would he have further developed any ideas / themes. Maybe you could post a new thread. Has this topic ever been done before?

That is strange! ya'll are right: Caspian isn't the true king of Narnia, because he is a Telmarine! whay would they mess this up so badly? oh, well. maybe they didn't think it was marring any part of the book!