The two favourites to progress from Group A - which also features Japan and South Africa - the pair have left some big names behind and brought largely home-based squads to Japan.
Following possibly the proudest day in Mexico's long football history at London 2012 - where El Tri were crowned Olympic champions after a dramatic final victory over Brazil at Wembley - they came back down to earth with a bump when exiting the 2016 tournament at the group stage.
However, victory in March's CONCACAF Olympic Qualifying Championship ensured the Central American nation would return to the summertime festival of sport for another attempt this year.
All but two members of Jaime Lozano's squad play their club football domestically, in Liga MX, but his final 22-man squad - announced earlier this month - features a number of players who are regular faces in the senior squad.
One of the Europe-based stars to be selected, Real Betis winger Diego Lainez has already established himself in Gerardo Martino's national team, with three goals in 14 games so far - including one against Panama just a fortnight ago.
Lainez had not been involved in the qualifying campaign and was expected to join Martino's squad for the ongoing Gold Cup, so his inclusion in the Olympics could prove a major bonus for former Queretaro manager Lozano.
During the run-up to this Games, his team have gone unbeaten through three friendly encounters - beating both Australia and Romania, plus drawing 1-1 with fellow finalists Saudia Arabia - to build hope that El Tri can emerge from the group and make it into the latter stages once again.
While France have won six international honours in all - two World Cups, two Euros and a couple of Confederations Cups - success has been much more elusive at the Olympics.
The only gold medal in Les Bleus' illustrious history came in Los Angeles, at the 1984 event, during one of the golden ages of French football. Since, though, they have essentially been absent without leave and they last qualified in 1996.
Amid much talk of even their second-string side being credible contenders for major titles, France's next generation has been largely omitted from the long journey east, as some were on duty at the Euro 2020 finals and others have been summarily withdrawn by their club sides.
Sylvain Ripoll's squad, then, is drawn primarily from Ligue 1's deep reservoir of talent, but veteran striker Andre Gignac and his new teammate at Liga MX club Tigres UNAL, Florian Thauvin, have been called in as over-age players.
In five seasons with Marseille before heading to Mexico this summer, former Newcastle United winger Thauvin registered 67 goals in 180 games for the French giants and, on Thursday, is sure to cause headaches for some of the defenders who will shortly be facing him in league action.
His coach, Ripoll, also led France to the semi-finals of the 2019 European Under-21 Championships, which earned Olympic qualification, but for various reasons has only seen three players from that tournament progress to his Under-23 squad.
Perhaps his experienced additions to a relatively untried side offer the greatest hope of causing a splash at these Games, with both Gignac and Thauvin feeling they have a point to prove in the absence of big-name stars.
Mexico's 114-times capped goalkeeper Guillermo Ochoa, who was in the 2004 Olympics squad and has been to four World Cups, has been included by coach Jaime Lozano, and the 36-year-old is set to start as El Tri's last line of defence on Thursday, though Luis Malagon played each of the three warm-up matches last month.
Diego Lainez and former Manchester City winger Uriel Antuna are poised to take their place on the flanks, with over-age striker Henry Martin expected to beat Eduardo Aguirre to the central striker's role.
Meanwhile, Sylvain Ripoll's plans for his France team were torn up in the weeks preceding this game, as much-admired Rennes midfielder Eduardo Camavinga was initially included alongside Arsenal defender William Saliba, but both were ultimately omitted after their respective clubs objected.
Not only have two key members of Les Bleus' central spine been left to watch from home, but Malang Sarr, Amine Gouiri and Maxence Caqueret have also been prevented from representing their country in Japan.
The French defence may have a makeshift look too, as Everton full-back Niels Nkounkou received a late call-up after Jeremy Gelin withdrew due to injury. However, Milan's versatile Pierre Kalulu is available and could forge a centre-back partnership with Modibo Sagnan.
Over-age forwards Florian Thauvin and Andre Gignac are favourites to start up front.
Mexico Under-23s possible starting lineup:
Ochoa; Er. Aguirre, Vasquez, Angulo, Sanchez; Antuna, Esquivel, Rodriguez, Romo, Lainez; Martin
France Under-23s possible starting lineup:
Bernardoni; Michelin, Sagnan, Kalulu, Caci; Toussart, Savanier, Le Fee; Nordin, Gignac, Thauvin
We say: Mexico Under-23s 1-1 France Under-23s
An intriguing clash of cultures is set to kick off Group A, as a particularly callow France side - which it would be generous to call even their third-choice selection - meet a more settled Mexican team.
Expect France's crafty Liga MX pair to cause problems though, and their contribution can help a cobbled together unit salvage a valuable point from a testing first game.