cycleway on sidewalk ?

In my city, there are cycleways on the road: I can use ‘cycleway=lane’ to tag them.
There are also cycleways on the sidewalk: 2 white lines are painted on the sidewalk and it’s supposed to be a cycleway (you can see an exemple of this french specialty here or here)
My simple question: how to tag that ‘cycleway’ in Osm ?
IMHO, I think Osm should add the value ‘sidewalk’ to the key ‘cycleway’ but it doesn’t exist presently.

Tag the road as cycleway=track
That means there is a cycleway next to the road, not on the road. it may be on the pavement/sidewalk, or it may be further away. See

Another option is to map the cycleway as a separate way, tagged as highway=cycleway (or highway=path). I think this is usually a good idea - it means you can show where the cycleway actually is, ie what side of the road and how far away from the road. Plus you can tag it with the surface, width, access tags etc.

According to “cycleway=lane” is correct, if the cycleway is part of the road. “cycleway=track” is correct for the other examples you posted.

Have a look on that: