Can I touch the metal frame or do I need to ground it?

I live in Eu and I connected the blue – neutral and the brown – hot to the light jack. There is no third ground wire in the cable and i am afraid to touch the black steel frame – is it dangerous, should I ground it or is it not necessary?

Please help

Edit and update:

I added new photos

I connected the blue neutral wire to the T210 and the brown wire to the OE50(or something like that) There is no label except class 1 insulation symbol on the light bulb socket and again class 1 on the electric cable and some others which I don't know what they mean.

No double insulation symbol so I guess I need to ground or buy a cable with ground wiring.

Here are the photos.

Update 2 and new related question.

I found out some celing lamp was wired as seen in photo. It is same level 1 insulation and the ground is not connected to nothing. Was that done wrong? Should I turn off electricity at the fuse box as precatution and connect green/yellow – ground wire to that steel bolt, would that ground it?