Campion was born in Lunéville (Meurthe-et-Moselle) in Lorraine to Jacques and Charlotte Bruget. We don’t know much about his early musical education in Lorraine, but perhaps, he was a student of Henry Desmarets. Given that his father was serving in the Lorraine court, his family was transferred to Florence, Italy at the same time as the rise to the throne of the Tuscan Granduca (Grand Duke) Francis of Lorraine in 1737. During this period of time, he presumably came into contact with Giuseppe Tartini, who we know for a fact was Campion’s teacher. From 1752 to 1762, Campion was Chapel Master of the Cathedral in Livorno. He was fortunate to be friends with some aristocrats, and succeeded in having his opera (Venere placata, libretto by Marco Coltellini) performed for the celebration in Livorno (at the Avvalorati Academy) of the royal wedding of Joseph II and Princess Isabella of Parma in 1760. On February 14, 1763, the Grand Duke, with no regard to the normal selection procedures, nominated Campion Master of the Court Chapel, which combined that of the Cathedral and the Baptistry. It is possible that father Giovanni Battista Martini advised the Grand Duke to nominate Campion; we know that Campion had been in contact with Martini previously (letters between the two men, who shared a passion for antique music, are conserved at the International Museum and Music Library in Bologna).
The employment of Campion followed the idea and desire to rebuild the court’s musical activities in Florence, which was intended to be reestablished by the Lorraines after the decline during the Reggenza period: an intention that became intensified with the new Grand Duke Peter Leopold. During his employment in Florence, Campion gained the respect of Italian and European cultural society for his taste and his collection of antique music. Charles Burney mentions him as a great collectionist in his The Present State of Music in France and Italy, affirming that his collection was second only to that of Martini. In the 1760s, he traveled abroad in order to promote the publication of his music. He printed his music in Amsterdam and Paris under his own supervision, and Walsh published his works in London. The Walsh editions were diffused worldwide and were highly appreciated by Thomas Jefferson, who became a great collectionist of Campion's compositions for violin, of which he even kept a thematic catalogue. In 1766 he married Margherita Perloz Brunet, a harpsichord expert and painter, to whom he dedicated some of his keyboard compositions. There is some information regarding his meeting with Wolfgang Amadeus Mozart, who at the time was only fourteen, in Florence in 1770.
In the 1770s, Campion was the protagonist of a harsh querelle with the Marquise Eugenio di Ligniville who was also from Lorraine and participated in the regeneration of the Florentine musical activities and supported the nomination of Campion to Master of the Unified Courts. Ligniville, himself, also gained from this nomination and received the appointment of Superintendent of the Music of the Real Chamber and Chapel. The nature of their contracts very clearly established the fact that Ligniville's concern was to ensure more complex performances, while Campion's task was to guarantee ordinary routine musical activities and administrative tasks. However, in 1772, perhaps driven by the desire for attention or by a competitive tendency unique to himself, Ligniville told the Grand Duke to not be satisfied by his superior musical status and accused Campion of not being able to manage the Capella, both economically and musically. This might have been an attempt to take Campion's job. The accusations were not supported by many in the Duke's court: Campion was well-liked by the Grand Duke himself and his officials. He succeeded in personally reacting to the attack, demonstrating his ability by writing the Trattato teorico e pratico dell'accompagnamento del cimbalo con l'arte di trasportare in tutti i toni e sopra tutti gli strumenti (a treaty of composition) dedicated to Peter Leopold (the autograph is found at the Conservatory in Florence). During the debate which lasted four years, Father Martini became indirectly involved, and although he was personally closer to Ligniville, Father Martini confirmed Campion’s talent. As a result of his excessive accusations, in 1776 Ligniville was stripped of his responsibilities and fired, while Campion remained in his position, and received many honors until his death in 1788.
Campion was a prolific composer and represents a trait d'union between the traditional composition methods and those of the Classical style. He composed many instrumental pieces for harpsichord and strings, which were mentioned previously as being extremely successful abroad for demonstrating an excessive chromatic style, surely influenced by his teacher Tartini. He worked very often with sacred music, in which on the contrary demonstrates a very rigid approach to counterpoint. Many of his sacred compositions originate from celebrations and the court: for example, the Requiem for the death of Francis I of Lorrain (1766, the autograph is in Berlin, see Source section); the Te Deum, written for the birth of the heir to the throne Francis II (1768), which required almost 200 performers; and the Requiem for the Florentine celebration of the death of Maria Theresa (1781), today in Vienna (see Sources). Oddly, we have no profane celebratory compositions by Campion if not the cited Venere placata for the marriage of Josef II, and the incomplete Etruria fortunata, written for Peter Leopold, which was probably unfinished because of Campion’s death (the autograph is conserved in Fiesole, see Sources). It is also important to mention the non-celebratory profane cantatas T'amo bell'idol mio, for voice and instruments (conserved at the Conservatory of Florence), and the epithalamic cantata written for the Pichi family, today in Ancona (see Sources).