Claire has two forms: the Mother Goddess, which is her modern incarnation, and Claire the Ancient, which is the person she once was before her deification.

The statue of Claire the Ancient is said to be all that was left of Claire "after she was purged of all evil."  Presumably it depicts her the way she was as a mortal.  Here's a picture, courtesy of the Klonoa wiki:

The statue of Mother Goddess Claire is supposed to be a modernized depiction of the individual.  Here's a picture.  (I took this one, so it's kind of shoddy.)

I want to throw a couple of close-ups in here, too, so lemme do that.

At one point in the game, Popka, one of your companions, asks, "Doesn't Klonoa remind ya, just a little, of the Goddess Claire?"  Lolo, your other companion, agrees that he does.  And I agree with both of them - and I also think that the game's final antagonist, the King of Sorrow, has some of the same traits as well.  I think they all have a lot in common with each other.

For the sake of comparison, please also accept these pictures of Klonoa and the King of Sorrow:

So, there are some design elements that pull the three of them together.  First, there are their rings.  In her Ancient form, Claire's hands are bound by a ring of some sort. She also has a curling pattern on her forehead which, when paired with the (often upside-down) triangle that seems to be her symbol, is reminiscent of Klonoa's Wind Ring.  The King's collar is his ring, and it sports a braided pattern which also appears on Claire in both of her incarnations.  (Klonoa also sported an outsized collar when he appeared in his first game, Door to Phantomile, which ties them together further.)

Second, those ears!  Klonoa and the King both have large, outlandish ears, a huge part of their designs.  Both of Claire's incarnations have something similar going on in the head region, and while it could ostensibly be hair in her Goddess form, I have to say I think she might share the crazy ear thing with both of the other characters.  The two structures on her Ancient form are so flat and clearly divided I can't read them any other way, either.  You could even say that the separated shapes in her Ancient form evokes Klonoa’s design and the consolidated sheet-like shapes in her Goddess form evoke the King of Sorrow’s design.

But, y'know, there are story things that pull them together, too.

We don't know much about Claire, honestly:

Thanks to Popka, we know she ascended to Goddesshood after being purged of evil.

Therefore, we can infer that her Goddess form is free of evil.

We know that one of her roles is to forgive people for their sins, as Lolo prays to her for forgiveness when she finds out Popka has stolen something.

Aside from the comparison Popka makes between her and Klonoa, those are the only two times she's even mentioned in the game.  But we can tell from the pictures that Ancient Claire was unhappy.  She's bound at the hands and frowning. Compare this to Goddess Claire, who is, if not happy, at least neutral and unbound (and apparently possessed of some amount of power if the sphere she’s holding is like Klonoa’s “wind bullets” or like the elements that reside in Lunatea’s bells).

I think - and I think it's pretty obvious - that the entirety of Lunatea is the story of Klonoa coming to terms with his sadness about the tragedy of Phantomile.  Especially in Luntea's final levels, I think there are details alluding to it everywhere.  Leading up to the fight with the King for example, you travel through the "Kingdom of Sorrow," also called "Hyuponia" - totally a nod to Huepow/Hewpoe from Phantomile.  The music in this level is like a radio station with terrible reception, but through the static you can hear snippets of songs from both games - Lolo's theme and also Grandpa's theme, the Windmill Song, and the Song of Rebirth.  It's very bittersweet.

Lunatea is also the story of historical events done all over again, but better - kinder.  Lolo, a clumsy outcast acolyte, is a counterpart of Leorina, a powerful priestess-in-training turned rogue sky pirate. Klonoa, the dream traveler who has had everything torn from him, is a counterpart of the King of Sorrow, who has no place in the world he once occupied after his kingdom and his very self are forgotten by people who don’t want to remember sadness. Leorina and the King are from an older time where each felt outcast and acted on their pain, and each wrought only further unhappiness and destruction. Klonoa and Lolo are from a newer time. They have no place that they can see on their own, but they have each other and come to move past the unhappiness that holds them back.  They forgive their circumstances - and when their old-world counterparts follow their example, they in turn begin to rebuild the things they destroyed.

In Klonoa’s case, when he moves past his pain - when he literally defeats [the King of] Sadness (and forgives the King for what he has done) - he becomes whole and clean. His actions have, directly or indirectly, resulted in a sort of “rebirth” as the kingdoms are being connected once more.  When he moves on from the world he helped, he does so not against his will (as in Phantomile) but with confidence and purpose, having really come into his own.

In the King’s case, when his overwhelming sadness is defeated and the terror beneath it is confronted, when he is forgiven, he is literally reborn: his body fades away into points of light and the pictures in the credits of the game show an infant  who could only be a baby King in the care of the High Priestess.  He is, so to speak, “cleansed of evil” and able to begin anew in an innocent form.