The Six Nations champions will tackle Tri Nations title holders Australia in a three-Test series that Wales coach Warren Gatland is already planning for.
Gatland has long accepted that success against southern hemisphere heavyweights Australia, New Zealand and South Africa is how Wales must expect to be judged on the world stage.
And Wales have only beaten the Wallabies once from nine attempts in Australia, and that was 43 years ago, while their last victory over the All Blacks came in 1953.
“Tri Nations teams tend to beat us, and we will definitely be targeting the Australia tour,” said Jenkins.
“They [Australia] have put us to the sword in the last two games we’ve played against them. It will be a different challenge for us again in June, and that is the big target for us.”
Jenkins, together with his current team-mates Adam Jones and Ryan Jones, have now joined Welsh rugby’s most exclusive club, taking up post-war membership alongside Gareth Edwards, Gerald Davies and JPR Williams as a three-time Grand Slam winner.
“Later in your career you cherish things like this,” added 31-year-old Cardiff Blues forward Jenkins.
“When you’ve won the first two [Grand Slams] you are always hoping you can win another one. You never forget the atmosphere when you are walking around the stadium at the end, that standing ovation. You never forget things like that.
“It is a good achievement to win three. The 1970s boys had the three, and there are not many people who have done it.
“People like myself, Adam and Ryan have not been used to going into games as favourites. We have always been the underdogs, but this team has got to the stage where we can now be classed as favourites.”
Wing Alex Cuthbert scored the only try of an enthralling battle to help the home side to their third Slam in eight years. The try helped Wales to a 10-3 lead at half-time while Leigh Halfpenny added the conversion and three penalties over the course of the 80 minutes.
All of France’s points came from the boot of half-backs Lionel Beauxis and Dimitri Yachvili. Indeed, French fans will be left frustrated by the lack of positive intent or creativity from their side.
Scorers for Wales: Try: Cuthbert. Con: Halfpenny. Pens: Halfpenny (3).
Scorers for France: Pens: Yachvili (2), Beauxis.
WALES: L Halfpenny, A Cuthbert, J Davies, J Roberts, G North, R Priestland, M Phillips; G Jenkins, M Rees, A Jones, AW Jones, I Evans, D Lydiate, S Warburton (c), T Faletau.
Replacements: K Owens for Phillips (63), L Charteris for Rees (63), L Williams for A Jones (63), R Jones for Warburton (40).
FRANCE: C Poitrenaud, W Fofana, A Rougerie, F Fritz, A Palisson, L Beauxis, D Yachvili; JB Poux, W Servat, D Attoub, P Pape, Y Maestri, T Dusautoir (capt), J Bonnaire, I Harinordoquy.
Replacements: JM Buttin for Poitrenaud (35), F Trinh-Duc for Palisson (53), V Debaty for Poux (44), D Szarzewski for Servat (44), Pierre for Pape (67), L Picamoles for Bonnaire (59).
Referee: C Joubert (South Africa).