The Empress Eugènie de Montijo disliked sex and barred her husband from her bedchamber following the birth of the Prince Imperial (Napoléon IV). She miscarried a three-month pregnancy in 1853, and gave birth to the Prince Imperial - heavily dosed with laudanum - after a two day labor, since the doctors tried to make the Prince Imperial to be the birthday-twin of his cousin, Napoléon II.
What if Eugènie hadn't miscarried in 1853 and instead births a Prince Imperial? And including a long-shot, she still gives birth to the OTL-Napoléon IV. The alt-Prince Imperial would be 18 (close to majority) by the time (if) the Franco-Prussian War rolls around. No fear, therefore, of a regency of the conservative-minded, ultramontane empress to undo the start of the "Liberal Empire".
Thoughts and opinions?