'Bâiller', 'bailler', and 'bayer' are pronounced exactly the same way. However, they have nothing in common.

'Bâiller' (with a circumflex accent on the 'a'), means to open one's mouth out of tiredness or boredom.

Flaubert uses it in L'Éducation sentimentale: "I yawned with fatigue at its dawn."

'Bailler' (without an accent), is an old verb meaning "to give".

It gave rise to 'le bail' (lease), 'le bailleur de fonds' (lender), and the flavorful expression "vous me la baillez belle!" (you're trying to fool me) which Hugo uses in Les Misérables.

Balzac, for his part, writes: "I will give you the initial funds." (César Birotteau)

'Bayer' (with a 'y'), means to remain open-mouthed (in astonishment).

Madame de Sévigné used it in 1671: "I wanted to go into the street to gape like the others." (in front of a fire)

Today, this verb only survives in one expression: "bayer aux corneilles" (to gape at the crows, i.e., to daydream), which is too often incorrectly written as "bailler aux corneilles"...

In summary, the three words are pronounced the same way but have three different etymologies and meanings:

• Bataculare (to open the mouth) → bâiller

• Bajulare (to carry, to hand over) → bailler

• Batare (to remain open-mouthed) → bayer

Now you know.