Theoretically speaking, nieces and nephews benefit from an allowance of 7967 euros on the value of donations received from their aunt or uncle (art. 779 V of the CGI). If you have no children of your own, your niece may also claim the 31865-euro allowance applicable to the donations. The donor must be under 80 and the donee must be of age (art. 790 G of the CGI).
If all these conditions are met, you can give her 39832 euros free of donation tax.
Please note: these provisions apply only to donations made to the children of the donor's siblings, and not to donations that are made to the children of the donor's spouse.
In addition, even if no donation tax is payable, the latter must still be declared within one month of the donation.