There is an etymological link: they both derive from Latin esse “to be”.

There is also a grammatical relation insofar as they share the same morphosyntactic features (tense, person, gender, number…).

One reason they appear less parallel than they are is that you chose an inverted French question structure but a normal Spanish declarative structure. French actually has a more exact analogue: c’est que.

As you note, the presence of ce here in the French and its absence in the Spanish is a difference to be expected due to Spanish’s being a pro-drop language, which means that the two phrases are more or less equivalent as far as the grammatical features. The subject is before the verb in French and baked into the verb in Spanish, but present either way.

The semantics are also similar, in that c’est que, when used on its own to begin a sentence, can also be used to introduce an explanation or reason why something is the case (ex. one, ex. two).

So I’d say they’re related.

If there is a divergence, it could be in the other possible meanings that the phrases have in their respective languages, and/or in the discursive value of the two phrases (register, frequency, connotation). These are both elliptical phrases that we can expect to generate a wide range of meanings, and they might not all overlap.

For example, in French, c’est que can also be used to indicate a result instead of an explanation. In “La vérité sur la vérité” (1977), Daniel Lavoie sings:

Si c’est pas payant, c’est que tu perds ton temps.

Tu perds ton temps is the result of something not being payant, not the explanation. Can es que express both relationships, too? That’s a possible place of difference.

Actually they sound more similar than they actually are, because “Est-ce” is two words (verb+pronoun) where “Es” (just the verb) is one. It’s really coincidence that they happen to be pronounced exactly the same.

As Luke Sawczak says, the French analogue to “Es que” would be “C’est que” (with the French “ce” being implied in Spanish), and those do have similar meanings. The “est-ce” inversion makes it a question in French, which accounts for the difference in meaning between “Est-ce que” and “Es que”.

Theoretically given the pronoun isn’t necessary in Spanish you could have “Est-ce que” being exactly equivalent to “Es que” for the same reason “C’est que” would be (except the intonation on “Es que” would make it clear you’re asking a question), but that would be if the term were used as “the question form of ‘c’est que'”, which is not its main role in French at this point; now it’s a marker of the interrogative in its own right. As such it has no equivalent in Spanish.

In French a regular question can start with Est-ce que…? In Spanish the question starting with ¿Es que…? needs necessarily another question and normally implies a negative aspect. For example: ¿Por qué estás en cama?¿Es que no te sientes bien? (Why are you in bed? Is it because you are sick?) or
¿Es que vas a seguir saliendo con Carlos? ¿Después de todo lo que te ha hecho? (Are you going to keep going out with Carlos? After all he did to you?)