Proudhon was sentenced to three years in prison and a fine of 3000 francs by the Cour d'Assises on 28 March 1849. The trial revolved around two articles written by him and published in the newspaper le Peuple on January 26 and 27. Georges Duchêne, the manager of the newspaper, was sentenced to one year and 1000 francs. The four crimes that Proudhon and Duchêne were accused of were exciting hatred between citizens, exciting hatred against the government, attacking the constitution and attacking the authority of the president of the Republic.

The paragraphs le Peuple that was used to sentence him for the insult against Bonaparte is fairly long, but the gist of it is that Proudhon considered Bonaparte a threat to democracy and the people. Proudhon called him a traitor and accused him of sabotaging the process of securing the republic established after the revolution of 1848 by - among other things - replacing republicans in the legal system with monarchists, persecuting the left, refusing economic reform and betraying his promises to abolish taxes. As a result the national assembly should debate his removal from office, because "the president, that is to say the monarchy, corruption, lies, privilege, capitalist exploitation, is impossible".

The national assembly did not have the constitutional right to remove the president. The prosecutor, Meynard de Franc, saw Proudhon's suggestion that the assembly should debate whether to take unconstitutional measures as an attack on the constitution.

Meynard argued that this was an attack on freedom and the constitution by encouraging the losers of the election to take up arms against the majority, which made the prosecution necessary for defending the results of the election. The accusation wasn't technically that Proudhon insulted Bonaparte as a person, but that he challenged his constitutional prerogative to exercise the authority of his office. Proudhon's defender, Madier de Montjau, said that the insult was against the person and not the presidency, and insulting the president isn't a crime. Proudhon himself argued that he had only discussed the non-immunity of the president according to the constitution, and that he shouldn't be punished for interpreting the law.

The jury found both of them guilty by a majority of eight to four. As for whether this was a normal sentence or not, the non-political aspects weren't seriously challenged even by le Peuple. Legally and factually, the outcome seems to have been reasonable. The sentence was well below the legal maximum of five years and 6000 francs. Madier criticised the laws themselves for being vague and authoritarian, but didn't say much about the way they were applied in this case except to say that the crime hadn't been proven without really clarifying this conclusion. He also implied that maybe they were actually being persecuted for respecting the constitution too much.

Sources:

The official newspaper of the French government, La Gazette nationale ou le Moniteur universel, 29 March 1849, page 2. The full report can be found here

And le Peuple, the newspaper in question, 29 March 1849, page 1-3. This report is much more detailed, and le Peuple also took advantage of the opportunity to quote both of the articles in question in full.