I used to play the tenor horn in a brass band in the UK, when I was a child, and I still have the instrument. It is a brass instrument in E-flat (mi bémol), and is a very common instrument in brass bands although is not found in the brass section of the orchestra.

I confess I have never known the French translation, so am I not 100% sure, but I have attempted to research it a little this morning out of personal interest.

The Oxford Companion to Musical Instruments by Anthony Baines (p.333)
"Tenor horn (Amer.: alto horn; Fr.: saxhorn alto, alto; Ger.: Althorn;(...)). Valved brass instrument, in Britain pitched in E♭, a fifth below the cornet, with the bell pointing upwards. a standard component of the brass band in Britain and used also in France."

(p.296)
"Saxhorn. Family of valved brass instruments patented by Adolphe Sax in Paris, 1845. They are the parents of most of the deeper-valved instruments of the present brass band (other than German). Still in France the alto instrument, in Britain tenor horn, is known in full as "saxhorn-alto"."

The British Brass Band: A Musical and Social History By Trevor Herbert, (p.169-170)
"Adolphe Sax, the Belgian-born inventor and maker of wind instruments who worked in Paris from 1842, met with considerable opposition when he took out a patent in 1843 covering the instruments which came to be known as saxhorns (...) After a time, similar instruments by other makers were frequently called 'saxhorns'. The tenor horns (or simply 'horns') and baritones of the present-day brass bands are tenor and baritone saxhorns."

Also looked at a few image searches, e.g.:
Jupiter JAL456L - this Yamaha instrument is a tenor horn and seems to be sold as "Saxhorn alto (mi bémol)" in France.