It is possible to give your niece up to €31,865 without her having to pay any gift tax, provided that you have no descendants (children or grandchildren), that you are under 80 years of age, and that your niece is of legal age on the date of the gift (Article 790 G of the French General Tax Code).
You may also give her up to €7,967 without any age condition.
Both allowances apply every 15 years.