Franz Ignaz Beck began violin studies with his father, Johann Aloys Beck, an oboist and Rektor of the Choir School at the Palatinate Court in Mannheim. He also learned double bass and organ, among other instruments, and eventually came under the tutelage of Johann Stamitz, the Director of Instrumental Music and leader of the brilliant Mannheim court orchestra. Beck's talents were quickly recognized and the Elector Carl Theodor undertook responsibility for his education.

Although some sources maintain that Beck left Mannheim to study composition with Galuppi in Venice, his pupil Blanchard wrote a more colourful account in which he claimed that Beck, a court favourite, fled the Palatinate after believing that he had killed his opponent (a jealous rival) in a duel only to learn many years later while living in Paris that he was the victim of a cruel hoax; his opponent had only feigned death. Whatever the circumstances of his departure, Beck certainly did live in Venice for several years for it was from there that he eloped to Naples with Anna Oniga, his employer's daughter. After his eventful sojourn in Italy in the 1750s Beck moved to Marseilles and became leader of a theatre orchestra. The date of his arrival in France is uncertain but he must have been well-known by reputation at least as more than twenty of his symphonies were published in rapid succession by Parisian firms beginning in the late 1750s. The title page of the six Op.1 symphonies describe him as 'Chamber Virtuoso to the Elector Palatine and pupil of Johann Stamitz'; the Op.3 title page adds 'and actually first violin of the Concert in Marseilles'. At least seven performances of Beck's symphonies are known to have been given in Marseilles in 1760-61.

Beck moved from Marseilles to Bordeaux where he continued his interest in the theatre, subsequently being appointed conductor of the Grand Théâtre. His duties at the theatre were combined with composing and teaching. Among his more prominent pupils were Pierre Gaveaux, Blanchard and Boscha. On 24 October 1774 he was appointed organist at St Seurin, Bordeaux, and his exceptional improvisatory powers won him great admiration from the congregation. Beck's fame, however, was not restricted to Bordeaux. Several sets of his keyboard works were published in Paris and Dresden; he travelled to Paris to attend the first performance of his remarkable Stabat mater at Versailles and his overture and incidental music to Pandore were performed at the Théâtre de Monsieur in 1789. Beck appears to have had little difficulty adjusting to the revolutionary climate; he wrote patriotic music during the Revolution, including a Hymn à l'être suprême and in 1803 the new government expressed its approval by naming him correspondent of music composition for the Institute of France.

The pioneering research of Hugo Riemann and Robert Sondheimer in the early Twentieth Century focussed new attention on Beck's symphonies, most of which date from early in his career (ca 1757-66). More recently, Barry S Brook has praised Beck's symphonies as being 'among the most original and striking of the pre-Classical period'. Among the most progressive traits in his later works are the regular use of wind instruments in slow movements and an increasing emphasis on thematic development. His taut, dramatic style is also remarkable for its employment of bold harmonic progressions, flexible rhythms and highly independent part writing.