>Invalidating a box could result in up to a thousand votes being discarded indeed, which is quite small though for a national election.

I don't know what are the typical margins of victory for French Elections. In the 2000 US Presidential Election, George W. Bush won the Presidency by a margin of 537 votes in Florida. If the US had implemented French style balloting, a single attack of this kind in a heavily Republican district of Florida could have easily swayed the election to Gore.

French elections are decided on ~40 million total votes. Margins are much larger than a thousand votes.

the box is invalidated. If enough boxes are unvalidated, the ballot is probably cancelled, and rescheduled.