He was perhaps the earliest apprentice of Nicolò Amati,[4] another important luthier in Cremona Italy, although other sources call this association into question as there is no census record showing his presence in the Amati household.[5] The lack of census records showing the Rugeri name may be explained by the possibility of Francesco not being an indoor apprentice, but one who lived and boarded at his own home while apprenticing.[6] Antonio Stradivari's name never appears in the census records of the Amati household even though he was also a possible pupil of Nicolò Amati and may have lived and boarded with his own family.

W.E. Hill & Sons note that the "unmistakable" handiwork of Francesco Rugeri can be found, in certain of Nicolo Amati's works, and just like Antonio Stradivari and Andrea Guarneri, Francesco from time to time included the words "Alumnus Nicolai Amati" on his labels, further adding to the evidence of his apprenticeship.[7] For example, there exists a violin labelled "Francescus Rugerius Alumnus Nicolai Amati fecit Cremonæ 1663".[8]

Nicolò Amati was the godfather to one of Francesco's sons, Giacinto (born in 1658 and lived only a few months), indicating that the two families at least shared a close relationship and close collaboration would seem likely.[9][10] Francesco later had another son whom he also named Giacinto, who was born in 1661.

Interestingly, there was a court case brought in 1685 by a violinist who sought relief from the Duke of Modena as a victim of fraud. In this case, the violinist and composer Tomaso Antonio Vitali, bought a violin purporting to be a creation of Nicolò Amati. Yet under the Amati label was the label of Francesco Rugeri. There was a price difference in those days of 3 to 1 on Amati vs. Rugeri violins, so this was a serious matter.[11] However, this case may also indicate that Rugeri, who was working in the shadow of the great Cremona makers—Amati, Guarneri, and Stradivari—resorted to a desperate act to make a sale.