Yes, but only in case of absence of Customs service at your departure point (late arrival or long queues at the airport are not good reasons).
You can receive the authorization (known as posteriori procedure) at a French embassy or consular service in your home country within 6 months of goods purchase date.
Some French embassies, such as in London and Washington, have a Customs Attaché who can carry out the posteriori procedure and electronically validate the tax-free form (see here for the full list of locations).
You will need to either present:
a confirmation that import duties and taxes have been paid, or
your travel documents, ticket, and all the unused items listed on your tax-free form.
Either box A of the tax-free form will be stamped or a certificate of goods presentation will be issued.
Take a full clear image of each page of the document or upload a pdf scan into the app before we can refund your tax.
Alternatively, you can request for posteriori authorisation by writing to closest applicable office at the direction régionale des douanes et droits indirects (DGDDI) depending on your departure points (see here for the full list of locations) and stating:
Reason for not getting Customs stamp upon exit from the EU,
Details of your exit point from the EU,
Include scans of your passport and proof of residency, tax-free form, and the transport ticket.
Evidence of export (either a certificate of goods presentation from a French consulate or embassy, or import duties payment receipt).
If your request is accepted, the tax-free form will be authorised electronically.