The French Rugby Federation (FFR) and the French National League (NRL) want World Rugby to lower the legal height of a tackle to waist-height after the death of another player this month.
Stade Francais academy player Nicolas Chauvin died after breaking his neck, becoming the third player to die after a rugby game in France this year.
A 17-year-old player was found dead in bed a day after injuring himself while making a tackle, while former France under-20 international Louis Fajfrowski collapsed and died in the dressing room after he was accidentally hit in the chest during a collision in a pre-season friendly for his ProD2 club Stade Aurillac in August.
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During a meeting in Paris between the three governing bodies, French rugby boss Bernard Laporte also suggested banning tackles by two players and head-on-head tackles.
The FFR have offered to trial the laws in their amateur competitions.
"Rugby must become a game of movement where avoidance overrides the impact" said Laporte. "For this, it is important to change attitudes and change the rules, especially on tackling.
"The FFR and the NRL have therefore proposed to World Rugby an evolution of the rules by lowering the line of plating at the level of the belt, prohibiting the two-player tackle and tackle head-to-head.
"The tackler will have to bend if he comes to tackle, at the risk of being penalised. We have also proposed to World Rugby to experiment with these new rules on our amateur competitions."
World Rugby trialled lowering the tackle height from the shoulder to the 'nipple line' at the World Rugby U20 Championship in France, and also the World Rugby U20 Trophy in Romania.