While it's true that air is generally transparent, it is also generally circulating and in constant motion (unless in a vacuum), which helps explain it's use in the English expression "up in the air" to mean "without foundation or actuality; uncertain; undecided; and unsettled," which meaning is also captured to a certain extent in French by the adverbial phrase "en l'air."
Although the above discussion might help explain why "air" doesn't have to mean only "transparent," it doesn't connect the word to "appearance," which is your question.
One non-etymologic (Laure has the etymology covered nicely) connection/explanation that I can think of comes from comparing and connecting the somewhat similar words (and their multiple meanings) "air" and "nature."
"Nature" can mean 1) one's characteristics/properties (appearance), but it can also mean 2) all the things surrounding us (humans) on Earth (including air).
"Air" can mean the natural substance surrounding us that we breath (connecting it to meaning #2 of "nature"), but it can also mean, as you note, one's general appearance (connecting it to meaning #1 of "nature").
"Air can also mean a melody, as noted by Iside and Laure, which reminds me of one of my favorite expressions: "L'air ne fait pas la chanson," which captures well, I think, the notion that appearances can be deceiving.
Regarding your edit concerning the possible connection between "air" and "aire" in French, I wouldn't dare to imply that the following applies to French, but according to several [legitimate?] sources of the etymology of English words, it is probable that the two relevant senses of the English word "air" (1-gas and 2-(appearance)impression/manner) actually came from two different source words (1-gas-from the [old?] French "air" and 2-(appearance)impression/manner-from the Old French "aire.")
Origin (of the English word "air": (from Oxford Dictionary)
Middle English (in sense 1 of the noun): from Old French air, from
Latin aer, from Greek aēr, denoting the gas.
sense 2 of the noun is from French air, probably from Old French
aire 'site, disposition', from Latin ager, agr- 'field' (influenced
by sense 1).
sense 3 of the noun comes from Italian aria (see aria).
The main modern sense of air, ‘the invisible gaseous substance surrounding the earth’ entered English via Old French and Latin from
Greek aēr. Aerial (late 16th century), meaning ‘a rod or wire by which
signals are transmitted or received’ and ‘existing or happening in the
air’, comes from the same source, along with the Italian word aria
(early 18th century). Aerobic (late 19th century) is from aēr combined
with Greek bios ‘live’.
The senses of air ‘an impression or manner’ and ‘a condescending manner’ (as in she gave herself airs) are probably from a completely
different word, Old French aire ‘site, disposition’, which
derives from Latin ager ‘field’, the root of English words such as
agriculture (Late Middle English). Airy-fairy (mid 19th century)
‘impractical and foolishly idealistic’, was originally used to mean
‘delicate or light as a fairy’. The English poet Alfred, Lord Tennyson
( 1809–1892), in his poem ‘Lilian’ ( 1830), described the subject as
‘Airy, fairy Lilian, Flitting, fairy Lilian’. See also gas
The possibility of this curious "split/converging etymology" of the English word "air" (and its different meanings) is also mentioned by the Online Etymology Dictionary/Etymonline
air (n.1) Look up air at Dictionary.com
[1)] c.1300, "invisible gases that make up the atmosphere," from Old
French air "atmosphere, breeze, weather" (12c.), from Latin aerem
(nominative aer) "air, lower atmosphere, sky," from Greek aer
(genitive aeros) "air" (related to aenai "to blow, breathe"), which is
of unknown origin, possibly from a base *awer- and thus related to
aeirein "to raise" and arteria "windpipe, artery" (see aorta) on
notion of "lifting, that which rises." In Homer mostly "thick air,
mist;" later "air" as one of the four elements. ...
[2)] 1590s, "manner, appearance" (as in an air of mystery); 1650s,
"assumed manner, affected appearance" (especially in phrase put on
airs, 1781), from French air "look, appearance, mien, bearing, tone"
(Old French aire "reality, essence, nature, descent, extraction,"
12c.; compare debonair), from Latin ager "place, field" (see acre) on
notion of "place of origin."
But some French sources connect this Old French word ["aire"?]
with the source of air (n.1), and it also is possible these senses in
English developed from or were influenced by air (n.1); compare sense
development of atmosphere and Latin spiritus "breath, breeze," also
"high spirit, pride," and the extended senses of anima. air (n.3) Look
up air at Dictionary.com
[3)] "melody, tune," 1580s, from Italian aria (see aria)
I apologize for taking up so much space here talking about English etymology, and again, I'm not at all claiming that this discussion applies to "air" in French, but the possibility of two different meanings of a single modern word originating from two different source words and merging into the surviving word as the other one disappeared does exist in English and perhaps it can provide you with some insight that will help you find the answer to your interesting question and its edit.