Usually the root vowel in signum (Classical Latin) in historical linguistics is considered long, despite its etymology and its further development in the Romance languages; that being said, the jury is still out. As it is common in historical linguistics, there is no ironclad evidence and it's a matter of how you interpret the available data.
Traditionally, it was explained as quantitative lengthening or qualitative raising (the latter view is adopted by Weiss 2020: 142, a very old idea btw), which is believed to have happened in the following environment
V > V̄ / ɳn (Meiser 2010: 79).
Meiser 2010 explains the seeming contradiction between the epigraphic, etymological, and Romance data by claiming that this change did not happen in spoken Latin ("Umgangssprache"), see p. 61 and 79 ("Im Vulgärlatein ist die Dehnung unterblieben"); Sihler calls this "a local or socially restricted tendency" (pp. 76-77).
Leumann 1977 (§127), citing some interesting evidence from Diehl's Altlateinische Inschriften
44 Poublilia Turpilia Cn. uxor | hoce seignum pro Cn. filiod |
Dianai donum dedit
CIL I2 42 s. 389 XIV 4270 De 3234 (bronzetafel aus Nemi)
353 C. Tertaus P. [f.] | Ciamus | basim fac., sígnum st[a]. | ex
s. c. coer.
CIL I2 2096 a XI 4092 f (Otricoli)
217 uecos Supn(as) | Victorie Seinq. | dono dedet | lubs mereto.||
queistores | Sa. Magio St.f.,|Pac.Anaiedio St(ati f.)
CIL I2 388 s. 408 IX 3849 Ri 98 D De 3814 (bei Trasaco am ufer des Fucinersees) 2 verschreibung fuer seiqn. = seign.? Ihm Rh. Mus. 57, 316
also cf. Weiss 2020: 142, and Lindsay 1894: 138-139 for some interesting ideas, Niedermann 1953: 72 "Les tentatives ... n'ont pas abouti jusqu'ici" (i.e. the jury is still out), or Sommer and Pfister 1977 "Die Verlängerung trat wohl nicht auf dem ganzen Sprachgebiet ein (so auch Buck, Cl R 15, 311 ff.); eine allgemein anerkannte Erklärung ist nicht gefunden" (100)
Wachter 1987 ("Altlateinische Inschriften") seems to propose the following: a long vowel in Old Latin SEIGNVM and a short vowel in Classical Latin signum, as reported in Sen 2015: 145, but I don't have Wachter 1987 at home, so I cannot easily check this myself.
As for the etymological dictionaries of Latin, de Vaan gives sīgnum (and it's not a typo in this case, it's his choice), so do Walde and Hofmann (Band II, s.v. sīgnum); however, Ernout and Meillet opted for signum.
Unsurprisingly, Meyer-Lübke prefers sĭgnum (it's his Romanische etymologische Wörterbuch, if you were wondering why)