De Gaulle is prevented from running due to a sudden return of his prostate cancer (dying within a few months of his retirement). He nonetheless secures the UDR's candidacy for his PM (Georges Pompidou). This is somewhat controversial, given the latter's lack of "old gaullist" credentials. However, the "old guard", as well as the left-gaullists ultimately respects the General's choice.
Gaston Deffere succeeds in gaining the SFIO nod over Guy Mollet's objections. He also succeeds in forging an alliance with the centre-right MPR (promising to name a MPR Prime Minister). This means, of course, a continuation of the Communist Party isolation, which prompts them to run a candidate (insert name here).
Minor candidates are up to you.
The gaullist movement implodes. Michel Fycking Debre gets pissed and runs as a "True Gaullist" dude against Pompidou, supported by a number of his fellow dinosaur. Likewise, the "left-gaullist" (dudes like Rene Capitant and Louis Vallon) breaks as well.
On the left, despite having been blamed for the 1968 defeat, Mitterrand is again the SFIO/His Clubs/PCF nominee.
Poher's still in.
The "Barons of Gaullism" are able to prevent Chirac and other Pompidolians from breaking the ranks and endorsing Giscard (whose candidacy never gets a steam outside of his "Independent Republicans" circle). Chaban-Delmas faces Mitterrand in a runoff.
Chirac is able to rally the UDR behind Prime Minister Pierre Messmer, who also faces Mitterrand in the second tour.
Michel Rocard is able to capture the PS nomination, effectively ending Mitterrand's career. Due to the former's more moderate views, there's no alliance with the Communists (as in RL).
Rocard becomes the PS candidate, over Mitterrand's objections. Although he's the left most popular politician, the Elysee may work covertly to sabotage him.
Balladur honores his promise to not run, which gives Chirac a full RPR support, except for a minor splinted candidacy of Charles Fycking Pasqua (cuz Chirac betrays da gaullist ideas!!11).
Without Balladur, Giscard, who has been searching for a job since 1981, actually is a candidate again.
That's one pretty conventional. No surprise: Chirac v. Jospin in the runoff.
Make up a scenario based on the far-right gunman succeeding, despite his clumsiness, in killing Chirac on the Bastille Day.