The 29-year-old was initially suspended by the Aviva Premiership side before being sacked 16 days later following an internal investigation.
Arscott was found to have met with brother Luke, who plays for Bristol, at the club's team hotel prior to Sale's 24-23 defeat on January 1.
According to a report conducted by the RFU, Bristol were made aware of Sale's defensive tactics ahead of the match, although there was no evidence of them altering their strategy as a result.
RFU head of discipline Gerard McEvilly said: "In determining what action should be taken following the investigation, we have taken into account that Tom Arscott has already paid a heavy price for his conduct in having been dismissed from his employment by Sale Sharks.
"These issues have arisen because of the inappropriate sharing of information while players were socialising in the same hotel before the match.
"Therefore, the RFU is strongly recommending to both clubs that all their players are reminded of their contractual and ethical obligations to their employing clubs and of the problems that may arise should confidential/inside information be passed between individuals."
Arscott, the scorer of 20 tries in 72 appearances for the Sharks, has been given a written warning by the governing body and told to undertake a World Rugby education module.