You determine the strength of the structure by measuring the size of the joists, the length they span between supporting beams or walls and how far apart they are spaced. When you have that info, you input those values on a span table. The AWC has a good one, but you can just post that info here and we'll let you know.

I'm doubting you will have a problem but better to be certain.
Yes, remove the parquet, and who knows what else is under there. 90 years could be many layers until you get to the actual subfloor, which in your case will be planking. From there you would install 1/2" bc plywood, then 1/4" cement board, then your tile. 1/2" plywood gets installed with the grain direction crossing the joist, 1/4" perimeter gap, 1/8" gap between panels, fasten every 6" around and every 8" within, and only to the planking, not the joists. Cement boards have the instructions on them, thinset under, screw with cbu screws every 8", tape the joists as you tile, also maintain the 1/4" perimeter gap.
'd like to remove the parquet floor and install tile (I have a little boy and a husband, if ya know what I mean)
Umm, no, I don't know what you mean. Hey Bud and Jaz, either of you feeling kinda like the Geico cavemen after that comment? Hey Cathrine, how do we know it's really not YOU with the problem? Nah, my daughter shares a bathroom with her 3 brothers. I'll leave it at that.