Well, there are two generations of Logans, and I don't know if there are different options for A/C for any of the generations so allow me to inquire further: do you have to manually move a lever to redirect the air (quite possibly in such a car which is designed to be inexpensive) or do you have buttons (which means motors are doing the job for you)? Additionally, I don't know how the air ducts are laid out in a Logan so there might be either flaps which hold the air back which goes through the A/C cooler core or which redirect the air to the desired air vents.
Either way, something (either a physical connector or a motor) inside your dash broke, and since we don't know if you want to/are able to fix it yourself I'd recommend visiting a workshop which can do a quick check and give you an estimate to fix it. When you have the diagnosis you can further search the internet for fixes if you want to fix it yourself.