From the stats I could find, there's a drop out rate of around 20% between the first year and second year. Then 85% success rate in getting in an engineering school.
Once they are in an engineering school, the drop out rate is very low (both for private and public schools).
There are some engineering school that include the preparatory classes (we call that integrated prepa, an example is the National Institute of Applied Sciences INSA my alma mater) during the first 2 years, in that case the drop out rate is around 20% during the first 2 years and then less than 1% after that.
For both type of preparatory classes (integrated or not), students who drop out change major to something else and get to transfer credits to their new major.
For medicines, it's different. Until 2020 everyone could do the first year of medicine but only 20% would go on to the second year. Students were allowed to redo it once and then had to change major. There are no private medicine cursus in France. This has now changed and I'm not familiar with the new system.
With majors like liberal arts, etc... University is free and the drop out rate seems to be almost 60%. So yes, for majors with easy admission and free tuition (very little skin in the game) drop out rates are high.
But for highly selective programs where admission is difficult, there's very little drop out once students actually get in.