You have found a fragment of a pair of eyeglasses, specifically an arm or branch of the spectacles as shown by the location of the marks. The rust could be from the hinge that attached the arm to the body of the glasses.
There are 2 marks: a guarantee for smalls of a hare head facing right, in use from 1819-1838, and a maker’s mark in a lozenge-shaped reserve.
The maker was Louis-Michel Crouvezier, eyeglass maker, working in Paris at 25 rue St-Martin. His mark was initials L.M.C. with a lorgnette (un binocle) as the symbol.
Crouvezier registered his mark 4 times: 1812-13, 1815-1816, 1817, and 22 September 1835. His mark was erased 24 February 1853. Your object was made 1819-1838, as shown by the hare head mark.
Crouvezier had a mark for silver plate, the initials LC in a square reserve, the same symbol, and the word doublé for plated.
He also traded as Crouvezier Frères (brothers) according to a trade journal, Almanach Azur.
See Arminjon v. I, no. 2283, p. 236 and no. 2467, p.252
Crouvezier had successors, although it is unclear what relation they had to him-sons, brothers, nephews? All used the same symbol.
1-Joseph Crouvezier, listed as an eyeglass maker at 301 rue St-Martin, registered 24 February 1853, the same date that Louis-Michel’s mark was erased. Joseph’s mark was erased 12 May 1868.
2-Louis Crouvezier also listed as an eyeglass maker at 119 boulevard Sébastopol, registered 13 May 1868, erased 18 May 1875, likely the successor of Joseph.
3-Crouvezier & Thuilleur listed as jewellers 48 rue aux Ours, registered 1875, with no end date given.
See Arminjon, v. II, no. 2381, p. 224; no. 2856, p. 264; no. 1102, p. 117.
Amazing what the marks on a scrap of metal can tell!