How did 'countenance' evolve to mean 'support or approval'?

[OED:] The extension of sense from ‘mien, aspect’ to ‘face’ appears to be English: compare French use of mine.

[ Etymonline for 'countenance (v.)' ] late 15c., "to behave or act," from countenance (n.). Sense of "to favor, patronize" is from 1560s, from notion of "to look upon with sanction or smiles." ...

[ Etymonline for 'countenance (n.)' ] mid-13c., from Old French contenance "demeanor, bearing, conduct," from Latin continentia "restraint, abstemiousness, moderation," literally "way one contains oneself," from continentem, present participle of continere (see contain). Meaning evolving Middle English from "appearance" to "facial expression betraying a state of mind," to "face" itself (late 14c.).

Please help me dig deeper than the definition, which I already understand and so ask NOT about. I heed the Etymological Fallacy. But what are some right ways of interpreting the etymology to make it feel reasonable and intuitive?

1. Particularly, how did the meaning (that I bolded) evolve?

2. OED doesn't answer 1, but how does its reference to French (which I quoted) matter here?

We can follow the development of countenance starting with the etymology of contain:

late 13c., from Old French contein-, stem of contenir, from Latin continere (transitive) "to hold together, enclose," from com- "together" (see com-) + tenere "to hold" (see tenet).

Moving step by step, through the etymology of countenance:

v.
late 15c., "to behave or act," from countenance (n.).
Sense of "to favor, patronize" is from 1560s, from notion of "to look upon with sanction or smiles."

n. mid-13c., from Old French contenance "demeanor, bearing, conduct,"
from Latin continentia "restraint, abstemiousness, moderation,"
literally "way one contains oneself,"
from continentem, present participle of continere (see contain).
Meaning evolving Middle English from "appearance" to "facial expression betraying a state of mind," to "face" itself (late 14c.).

1. Noun formation from continere by way of continentem to continentia:

   • literally--the way one contains oneself
   • restraint, moderation

2. Generalization from restraint to Old French contenance: conduct, bearing, demeanor

3. Generalization from demeanor to Middle English countenance: appearance.

4. Specialization from appearance to facial expression.

5. Generalization from facial expression to face.

6. Verb conversion from conduct to Modern English countenance: behave, act.

7. Specialization from behave and facial expression to favor.

The final step of the verb to favor, was driven by the particular facial expressions of favor, which are an intuitive factor in the interpretation of behavior.

I believe we derived it from the phrase to keep someone in countenance, which means to help someone to remain calm and confident, or sort of to help them retain a good face.

The word countenance comes from the Old French word coutenance meaning ‘bearing, behavior,’ from contenir, from which we also derive the modern word contain. Contenir comes from the Latin continere whose meaning can be broken down into two parts. The first being prefix con- which comes from the Latin word cum meaning 'with' and then the second being the Latin word tenere which means 'to have (or to hold)'. The early sense of the Old French word coutenance was ‘bearing, demeanor,’ also ‘facial expression,’ hence ‘the face.’

P.S. the present (active) participle of continere is continens, continentem in the unnecessary inflection of continens into the accusative masculine singular (also I have no clue why they [the website refrenced above] would choose the accusative masculine singular, it would be easier to give it in its simplest form)

From an enthusiastic Latin student