Well, if you assume that the Major Magical Focus covers spirits from all 10 of the forms, then an Elemental Spirit focus would cover 40% of that. So, it depends on how large you consider the "Spirit" MajMF to be - if it's on the small side, then yes: 40% of a small MajMF would be a MMF. If it's on the large side, then no: it would have to be 20% of a large MajMF, rather than 40%.
Personally, I'd say yes on the MMF - the MajMF is covered by a handful of Vim guidelines that seem to put it just outside a MMF; As such, taking less than half of that definatly bumps it down into MMF, for me.
You don't actually say what the focus in Elemental Spirits encompasses.
From the 5th Ed book, a Minor Magical Focus should be smaller than a single Technique and Form combination.
Even a MMF in Healing involves a very limited aspect of the Technique Creo against 3 forms - Corpus, Animal and Herbem.
Likewise, the Major Magical Focus should be smaller than a single Art.
So I guess the question is, does the focus in Elemental Spirits involve a single Technique, or multiple Techniques?
If only a single Technique, then like Healing you should have a Minor Magical Focus.
But if you get the bonus for Rego, Perdo and Intellego (for example), then I would say it is a Major Magical Focus.
Just chiming in to note that a major focus is supposed to cover less than half of a Form, while a minor focus is supposed to cover less than a Technique+Form combination, i.e. less than a fifth of a Form. Now, (1/5)/(1/2)= 4/10.
Of course, I think one should also eyeball the relative usefulness of a focus to other focuses. I think "spirits" is a smallish major magical focus, compared to e.g. the minor focus "beasts of legend" that Bjornaer's Mythic Blood grants. So I think "elemental spirits" is fine; in my saga there's a character with a minor focus in "chthonic spirits" covering all spirits associated with death, evil, the underground etc. which seems roughly comparable. On the other hand, elemental spirits seems a disproportionally wide focus compared to other canonical minor focuses like "the colour purple" or "mustelidae"...
In canon, Minor Magical Focus (Elemental Spirits) does exist. The Corrguineach tradition from Ireland, presented in the "Ringing the Changes" sidebar for the House Ex Miscellanea chapter in HoH: Societates are mechanically equivalent to the sahirs, and that's their minor Miscellanea virtue.
There are two Magi from that tradition in "Through the Aegis", fully described.