Morgan Caron, an official for the French motor sport federation FFSA, said the initiative to show the F1 drivers' support was championed by Bianchi's French compatriot Jean-Eric Vergne.
Caron told France's RMC Sport: "Jean-Eric was deeply affected by what happened and good friends with Jules, so he took the initiative to make a sticker.
'EVERYONE WILL SUPPORT JULES'
"It will be distributed to the entire paddock at Sochi. In GP2, GP3 and F1, everyone will support Jules with a small message during the weekend in Russia."
As was the case when Michael Schumacher lay in a coma earlier in 2014, publications and fans are now turning their hopes to the words of medical specialists after the nature of Bianchi's serious head injury was revealed.
One such specialist, Japanese Shinji Nagahiro of the university of Tokushima, said the wait for more information about Bianchi will continue for some time.
Nagahiro said: "In general a prognosis cannot be given earlier than one month after the accident but it may take longer."
It has been revealed that Bianchi suffered a diffuse axonal injury, and Nagahiro said: "The patient may regain consciousness and recover completely, or suffer after-effects.
"It all depends on the severity of the injury and the location of the damage."
Stay with Wheels24 for the 2014 Russian GP weekend.