The "Gaullists" as a political group used to refer to the Union des Démocrates pour la République.

Since de Gaulle's death, and the break-up of the UDR, the exact meaning of Gaullism is somewhat unclear. In 1980s-1990s usage, "Gaullism" referred to the Rassemblement pour la République (now integrated into the Union pour un Mouvement Populaire), Jacques Chirac's center-right party. Chirac has, in the past, adopted both dirigiste and laissez-faire approaches to economics; he now has a pro-European (pro-European Union) stance after famously denouncing europeanism in the Call of Cochin. For these reasons, some on the right, such as Charles Pasqua, denounce Chirac and his party as not being "true Gaullists".

There are people on the Left who also call themselves Gaullists. Even socialist president François Mitterrand, who denounced de Gaulle's way of ruling as a permanent coup d'état, was very intent on keeping the nuclear deterrent and asserting France's independence.

There are two other main tendencies on the right: the Le Pen, Vichy extreme-right, haters of De Gaulle since WW2; and the centrists, once led by former president Giscard d'Estaing. This group (the party is called the UDF) is not as influential as it was in Giscard's time, the '70s. It's now led by François Bayrou who is trying to make room for himself (for the presidential) by distancing himself from the "Gaullists", who are in government.

The two great individual figures of the post-WW2 French political scene are undoubtedly De Gaulle and Mitterand. By openly affiliating herself to Mitterand, Royal is making a bold declaration of what she claims is her capacity and stature. Mitterand was neither an ideology nor a policy buff, so it doesn't count on Royal's part as a declaration of intent in either of those fields.