Can the Shimano front derailleur prevent a gear of my bike from working? I recently bought a used rigid mountain bike, I'm very happy with it but I realized yesterday that I couldn't access the smallest chainring.

This one has a total of 3 front gears, but only numbers 2 and 3 are accessible.

I tried to adjust the Shimano but nothing works, I can't use chainring 1. (I am a beginner not an expert) 

Can the problem come from the Shimano? Should I look at something else?

Note: bike reference: B'TWIN Rockrider 5.0



Photo from priceminister.com
Your front derailleur is probably just badly adjusted, although there may be issues with the shift cable or housing, or potentially even the shifter. 

I'm not sure if by 'chainring 1' you mean the innermost or outermost. If outermost the cable is probably just too slack so the shifter cannot pull the cage outward enough. If innermost something is preventing the cage from swinging inwards, perhaps too much cable tension or something is jamming it.

Adjusting front derailleurs can be a bit tricky as cable tension, limit screws and alignment all potentially have to be dealt with. Park Tool has a good series of videos on derailleur adjustment that walk you through the steps and explain what each adjustment does. Front derailleur video is on this page. It's a good idea to go through these steps as if the derailleur has been knocked out of alignment no amount of adjustment will fix it. 

You can work through that but it's not entirely guaranteed to produce success. If you are a real bike novice find a good local bike repair shop and have them fix the problem. It would be a good idea to have them check the rest of the bike at the same time, especially brakes and rear shifting.