This an interesting phenomenon that actually did occur with all Romance languages to different degrees, not solely French. The phenomenon of ''re-latinization'' is often a stronger term for what actually happened, aside from the Romanian context which was more preeminent, and operated a little bit more forcefully with languages having a linguistic superstratum like French, Spanish and Romanian (Romanian making the biggest 180 after a strong morphological change in their language, namely declensional patterns which they got from Slavic influence and not Latin as Vulgar latin was down to three cases and two distinct declensional endings).
The example you give isn't one of them, however. Quite the reverse, actually. The circumflex accent is actually a diacritic from Ancient Greek which indicated a hiatus (linguistic pause) as a remnant of the forgotten ''s'' often dropped when it was followed by a consonant, especially when followed by a t (difficulty to follow the s sound when followed by a consonne occlusive alvéolaire sourde, more often than not because of the articulatory defect exacerbated because of the Frankish superstrate influence. Ironically, it was integrated in the French orthography when people had stopped respecting the hiatus, but this is more of a detachment from Latin than anything else.
There are lexical, morphological and even etymological examples which give an understanding of relatinization for Romance languages, the lexicon being one they all share.
For instance, "doigt" French for "finger", was spelt, after linguistic transformations from the original Latin word (DIGITUM), -doi. Through etymological hyper-correction, some grammarians reintroduced the /gt/ as a graphical remnant of the Latin influence. This is a form of relatinization.
One all Romance languages share (and English!) is lexical reintroduction through doublets and triplets. For instance, the word "people", peuple, pueblo, popolo, etc. all come from the Latin word (POPULUS), late and archaic Latin already suffering from linguistic truncation <POPLUS.> Instead of creating new words with existing particles or compounding particles, we decided to give a new meaning to the original Classical Latin word and keeping it closer to the original orthography, (POPULUS) giving respectively: Population (ENG), Population (FR), población SPA, populazione ITA, etc. These are forms of lexical relatinizations, or "latinization" for ENG as it isn't a Romance language per se.