The oldest word in each row (and likely source of the others) is in bold. Like everything in etymology, this is all tentative. Most claims (save for Por.) are from etymonline.com; many could be disputed.
|red||read||ruber||rubro ?, roxo||rojo||rouge||rudhira||*reudh-|
|carmine||carminium||carmim?||carmin||kṛmi-jā or just kṛmi|
|crimson||cremesinus||carmesim ← cremesin||cramoisi||kṛmi-jā|
|vermilion||vermiculus||vermelho , vermelhão||vermillon ← vermail|
|scarlet||sigillatus||escarlate||écarlate ← escarlate|
|cerise (cf. cherry)||ceresia||cereja?||cerise ← cherise||kerasia|
|burgundy||vinho , borgonha (cf. bordô )||bourgogne|
|(none; cf. garnet, grenade)||granatum||grená||grenat|
According to etymonline.com, *reudh- is “the only color for which a definite common PIE word has been found”. Red was considered the most basic color (after black & white) in the famous Berlin-Kay linguistic study, though by now its methods and conclusions have been very disputed.
“Color” doesn’t always mean the clear-cut concept of today’s designers and technicians. Color names in the past would be determined from accidental, unrelated criteria including the name of pigments, dyes, methods of production, fabrics &c. Today we borrowed the old names (and created new ones) to designate specific points in a color-space, usually defined in terms of the dimensions of hue, saturation, and value (or equivalently as RGB, CMYK &c.). Such definitions ignore transparency, reflection, light emission, texture and other visual features, but that is by no means universal; e.g. John Lyons showed that the basic color words in Hanuno’o are defined in terms of value and shininess (matte vs. glossy).
Even if we think of color as strictly HSV, it’s still a simplification to define each name as a specific point. For one thing, linguistic usage by natives is much wilder and more varied (so “burgundy” will be used not for a single point but for a large range of shades, depending on the speaker). And even if you do assign a specific official point for a color name (using a predefined scheme such as Pantone, HTML, or X11), there are still questions about your computer monitor’s gamma, temperature of ambient light, subjective perception interference by nearby colors and so on.
Color is hard! The color samples above are vast oversimplifications. I used the language-specific wikipedias as sources for the specific values; often they’ll just copy en.wikipedia, so that they might not represent native speaker’s understanding and that agreement in the table can be misleading.
French marron may be from a local language, or from Gr.; it originally referred to sweet chestnuts. Its cognates have come to mean “brown” in Por., “dark red” in Eng., and “chestnut” (the nut, not the color) in Japanese.
Scarlet ← sigillatus made a nice round-trip from the original L. to medieval Gr. to Arabic languages (Persian säqirlāt, Arabic siqillat) back to Europe.
The basic word for red in Por. is vermelho, not rubro or roxo as one would expect. In Old Fr. the original Latin word changed to an (augmentative?) form (vermillon ← vermail ← L. vermiculus), but the meaning was always the specific pigment/tone (vermillion). In modern Por. both regular and augmentative forms occur, but only the latter (vermelhão) refers to the pigment.
The base word for red in Sp. is a *reudh- cognate, rojo; but its Por. descendant roxo has come to mean “purple, violet”.
There are two critters that are historically important for the production of red dyes. European peoples had long used the kermes bug, which feeds on the kermes oak. Exploration of the New World in the 16c. brought the much more productive Cochineal insect used as a dye by native Americans, which quickly superseded the kermes. The Fr./Sp. word cochenille, applied to the new dye, probably came from L. coccum (cognate to Eng. cocoon), itself from Gr. kokkos, “berry” (supposedly because they initially assumed the dye was produced from fruits, though this explanation sounds a tad just-so to me).
“Carmine” (carminium, carmin, carmim) would become associated with the cochineal pigment and “crimson” (cremesinus, cramoisi, carmesim) with the kermes pigment, but in history things are more confused. The word families of “kermes”, “crimson” and “carmine” all came from related Arabic sources, and ultimately from Sk. kṛmi-jā “insect-derived”, from kṛmi “worm”. Were they interchangeable at first? Carminium was further influenced by L. minium, cinnabar.
Cinnabar or vermilion are mineral pigments (mostly HgS or Pb₃O₄) known since pre-history, and produced alchemically by the Chinese since the 8c. (the “China red”). The “vermilion” family of cognates had semantic drift; like kermes/crimson/carmine, it originally meant “[of] worms”.
Greek kerasia originated words for a fruit and a color. In most languages they’re the same, as in Greek, but in English they broke apart as cherry and cerise.
From the Burgundy wine one gets the color words bourgogne (Fr.), burgundy (Eng.), borgoña (Sp.); in Jp. it’s called simply wine-red. Por. uses two wines for colors: borgonha (uncommon) and bordô ← Bordeaux (common), though it can also just call the color “wine”, like Jp.
From L. pomum granatum “apple with seeds” one gets Eng. pomegranade and Fr. grenade ← grenate ← grenat. Due to semantic extension the cognates in various languages can mean the pomegranate fruit, the garnet stone, a shade of red, or a modern weapon (which resembles the fruit).
[…] Otud ide crvena krava,
Crveno telo otelila,
Crveno mleko podojila.
Otud ide crvena krava,
Vode devet crvenih pilicá,
Padoše na crveni bunjak,
Pokupiše crveni crviči.
I odneše preko mora,
Preko mora bez odmora.
(Out of there comes the red cow,
She gave birth to a red calf,
She nursed it with red milk.
Out of there comes the red hen,
She leads nine red chicks,
She fell upon a red dung-heap,
She gathered up red worms,
And she carried it off across the sea,
Across the sea without delay…)
—Bajanje South-Slavic healing poetry-spell, as reported by J.M. Foley.