Bastareaud had originally said that he was assaulted by four or five men, but later he admitted he had fallen over in his bedroom because he had been very drunk.
CCTV evidence had shown that Bastareaud had walked into his hotel unharmed.
Mr Fillon was disgusted by Bastareaud's actions, especially considering that until the truth had been revealed, Mr Key had apologised for what was believed to have happened in his country.
However, after receiving Fillon's letter the New Zealand prime minister's spokesman said the apology was appreciated.
Bastareaud, who had returned to France from Australia on Monday, had cuts on his face and very bad bruises that he claimed were the results of an attack.
The president of Bastareaud's club, Stade Francais, has susequently revealed that the disgraced rugby star has gone into a French psychiatric hospital.
