What is the meaning of the phrase "to mop and mow"?

I am trying to translate into French the poetic text "The Firstborn", by British author Laurie Lee, a text about the birth of his (second) daughter – Jesse/Jessy – on 30th September 1963. He writes:

"New-born, of course, she looked already a centenarian, tottering on the brink of an old crone's grave, exhausted, shrunken, bald as Votaire, mopping, mowing and twisting wrinkled claws in speechless spasms of querulous doom."

Obviously, the poet plays with/on (?) the verb phrase "to mop and mow", whose meaning I cannot find on any online dictionary... that is the problem with phrases... very often, dictionaries give you the meaning of words, rarely phrases! (Stupid websites: when you enter a search, they all raise their hands: "Me! Me! Ask me!", like eager students... and when you click on the websites, they just answer "I don't know!"!!!)

I am asking you, people, what, then, since – luckily – people are more knowledgeable than websites, is the meaning of the verb phrase "to mop and mow"? Obviously nothing to do with "to mop your brow" and "to mow the lawn"... ?!

The full OED entry for mop (Brit. regional in later use) is...

A grotesque grimace or grin, as made by a monkey. Chiefly in mops and mows.

You'll have to wade through a lot of hits for some eponymous "Arcade Puzzle Game" if you Google the phrase, but I assume the meaning is now clear enough.

Actually, I Googled far enough to discover that it goes back at least to Shakespeare's The Tempest:

Before you can say 'come' and 'go,'
And breathe twice and cry 'so, so,'
Each one, tripping on his toe,
Will be here with mop and mow.
Do you love me, master? no?

("modernised" here as ...tripping over his own toes, making funny faces)

OED says mop was "apparently formed by inversion" from mow = make a grimace (cognate with French moue = mouth, leading to English moue = pout). And yeah - babies do scowl and pout!

Following up on FumbleFingers's enlightening answer, I offer this entry from Charles Mackay, A Glossary of Obscure Words and Phrases in the Writings of Shakspeare and His Contemporaries (1887):

Mops and Mowes. Ill-natured mockeries and grimaces.

[Previously cited lines from The Tempest omitted.]

Mine uncle is King of Denmark, and those that would make mowes at him while while my father lives.—Hamlet, act ii. scene 2.

Apes that mowe and chatter at me.—Tempest, act ii. scene 2.

Spenser wrote mocks and moes, from which it has been supposed that mopes and moes was a corruption of mocks and mouths. Mr. Staunton glosses mowes as "ridiculous antics." The French has faire la moue, to make a grimace. Mop is said by Nares to be from the Gothic mopa, ridicule. Bescherelle, in his French Dictionary, has it that moue is derived either from the English mouth or from the Greek μναω, to press the lips. How wrong all these guesses are will appear from the Keltic màb or màp, to vilify, to rail, to employ abusive and scurrilous language; and mùch, mùg, or mùig, surliness, gloom, moroseness, or an illnatured contortion of the mouth and countenance. In the old French, called "Langue Romane," mouard and mouarde signify a male and a female monkey.

And these from Alexander Schmidt, Shakespeare-Lexicon: A Complete Dictionary of All the English Words, Phrases and Constructions in the Works of the Poet, volume 2 (1886):

Mop, subst. a grimace; joined with mow: each one, tripping on his toe, will be here with mop and mow, T[em]p[est] IV, 47.

Mop, vb. to make grimaces; joined with to mowe: Flibbertigibbet, (prince: of moping and mowing, who since possesses chambermaids and waiting-women, L[ea]r IV, 1, 64.

...

Mow, subst. a wry face, a grimace: will be here with mop and mow, T[em]p[est] IV, 47. those that would make mows at him while my father lived, H[a]ml[et] II, 2, 381 (Qq mouths) contemn with mows the other, Cymb[eline] I, 6, 41.

Mow, vb. to make faces: apes that mow and chatter at me T[em]p[est] II, 2, 9. mopping and mowing, L[ea]r IV, 1, 64.