I am Bangladeshi currently in France applying for a Spanish visa. The visa office will hold the passport for few days. Is it possible to travel during this time?
Travelling internationally without any travel document is between very difficult and impossible depending on the details. If you need to leave the Schengen area and re-enter, you definitely need a passport. You would in all likelihood be refused boarding by the airline or blocked from leaving the Schengen area by the border guards.
If you are travelling within the Schengen area and have a residence card, it might still be possible in practice even if it's not explicitly allowed. If you have nothing at all, you would probably still be able to physically cross the border but could get in serious trouble if you are found in another country with no document establishing your status.
Even travelling in France is not without risk. Technically, you are supposed to be able to prove you are in France legally (i.e. show your visa) at any time if the police asks. If you don't have your passport on you, they could detain you for some time to check your status.
Obviously, the requirement to surrender your passport for a visa application puts you in an awkward situation but there is no easy way around that.