I'll give a short answer not as an historian but as a frenchman with a modest knowledge on the subject: Basically, following the liberation of France, the political legitimacy came from who was a part of the resistance. De gaulle (who gathered a considerable popular support) instituted from the start of the liberation an administrative hierarchy answering to the temporary government of france (with himself at its head). There was some friction with the communists, who basically were the only ones to have enough legitimacy to be able to contest de gaulle and who had separates resistance networks and with the american leadership (roosevelt) who wanted to institute a temporary allied-governed france. In the end de gaulle prevailed and led the independant government of france until the next election of a constituante assembly in 1946, which elect de Gaulle, who want to avoid a return to an unstable and short-sighted parlementary regime and is a proponent of a presidential regime. But the political parties don't support him and he give its demission hoping that it would create a massive popular reaction and make his opponents give up. It doesn't happen, the IVth republic (a parlementary regime) is instaured and de gaulle, too stubborn and proud to come back on its decision will stay out of the political scene for 12 years, until the algerian crisis allow him to make its come back in 1958.
As for the political and administrative responsables/officials during vichy, a substantial number of locals were lynched, some were arrested and executed. But Those able to flee and/or stay under the radar for some times (two or three years) were generally unpunished, as France government chose to put all this shamefull collaboration stuff under the rag after the initial purges.
On collaborators: France went through a process called epuration sauvage and epuration legale (excuse my French). The former saw Germans, women who slept with Germans and officials put into carts, shaved, paraded around the town and lynched. The epuration legale came after when the new establishment realised that a nation could not be rebuilt under such savagery, after all what would seperate them from the Nazi's if they did this?
The leading figures mostly escaped, a lot to South America, and were in turn recruited by intelligence agencies. Some were found, most never were. Interestingly those who were found and tried were often subject to witness statements from Historians who had studied the period.
By the late 1950's most of those incarcerated were released. The most interesting prisoner was Marshal Petain, leader of Vichy France. He was known as a soldier in WWI for being the Victor of Verdun, as it was under his guidance the French forces repelled the German attackers, but he soon became the Villain of Vichy.
Follow-up question: What happened to the blatant government officials in Vichy France that worked with Nazi Germany after it dissolved? Were they publicly shunned in France?