Can I drill into the handles of a B'Twin 100 Arctic?

Awwww :)

I think if you're only drilling into the ends and not into the span of handlebars, it should not be a big problem. But it would be easier to mod the tassels to fit the bike than modding the bike to fit the tassels. Cut the bit you are supposed to stick into the tube off and glue them to the ends, or to the handles themselves.

If you still want to drill it, try it out. That should show what the material is. Just use a small drill and look what kind of chips are coming off.

My guess is the bars are not solid. The likely cause is a plastic plug in the bar end. The plug was installed then the grip covers the the cap and the bars. The plastic in the end cap tends to be much stiffer than the plastic the grip is made of. If you drill a hole the same size as the grip has the plastic screw on the tassel won't fit in the hole because the hard plastic won't stretch. My suggestion would be remove the grip. Drill a hole in the end cap slightly larger than the plastic screw. Reinstall the grip then install the tassel per the instructions.

Drilling into the plastic end-caps is fine. Drilling into the bars is usually not. At the very end of the bars it should be fine. Somewhere in the middle it could cause stress raisers that lead to failure of the bars.

The bike in the picture has big concertina like bumpers at the end of the bars. Whatever your modifications are, you need to keep those bumpers, and keep them reasonably soft (ie glue good, plastic screws ok, metal screws bad.). When children fall on those small bikes the wheel often twists the bars and the child plunges directly into the bars. When the ends are not protected the bars become as dangerous as spears. This is not a rare or freak accident!

I've seen one accident that caused very painful, but hopefully non-serious, injuries. (Unfortunately the parent did not deem it necessary to have the child checked for internal injuries in hospital). In another case I saw a 4 year old miss the jugular by a few millimetres, ending with a deep scratch next to it mitigated by the helmet strap. What is more, I read of cases where bars without plugs caused deadly injuries.