In a French song, what does "Alors rangeant sa gapett'" mean? The song is "Mimile".

Roughly, "alors rangeant sa gapette" would mean "so, adjusting or tidying up his gapette"; a gapette is a kind of headwear worn by cyclists. I haven't been able to locate written lyrics to put it in context, which might make a more elegant translation possible.

https://fr.wikipedia.org/wiki/Gapette

To supplement the previous response, the lengthy lyrics to Mimile (describing the exploits of a debonair man) are found at https://www.paroles.net/maurice-chevalier/paroles-mimile-un-gars-d-menilmontant.

Son départ s'est fait sans bruit
On avait besoin d'lui
Pour un autre métier
Alors rangeant sa gapette
Ses ch'mises en satinette
Couleur de rahat-loukoum
Il rejoignit l'premier jour
Mais en blaguant toujours :
"J'm'en vais au badaboum"

Rough translation:
His departure was silent
We needed him
For another job
So putting away his gapette [cycling cap]
His sateen shirts
The color of Turkish delight
He joined the first day
But still joking:
"I'm going to the badaboum"


Before helmets became the norm, two types of gapette were worn for cycling, one kind of a mini baseball cap, while the other is familiar from Peaky Blinders. The small, light version can still be worn within a helmet. https://fr.wikipedia.org/wiki/Gapette, https://lebob.fr/blogs/casquette/la-gapette, https://www.ouest-france.fr/leditiondusoir/2022-10-31/a-24-ans-ce-jeune-entrepreneur-reve-de-poser-sa-gapette-francaise-sur-la-tete-des-professionnels-d00c7165-3080-4c03-8412-63589892d1cb