Based on the reference pics i think you should be ok with basic red , crimson is a more "pinkish " red.
for the crimosn i use Magenta and a dab of napoleonic red.
Depends with regiment of Line Chasseurs this figure represents... Could be red, crimson, rose... Also, depending on the regiment, the facing colour would be shown on collar and cuffs or just cuffs etc. Its layed out in detail in the Rousellot book, I can forward it if you want.
In case it's of any help to Steve and others, a quick bit on some of these colour/hue names.
Scarlet = orange-red, so anything scarlet should be at least a little orangey.
Crimson unfortunately varies a great deal in how it's defined, but for uniforms it's often a little to the magenta side of middle red, i.e. closer to rose; need to be careful here though, in paints crimson is usually not more magenta-ish, just darker.
A visual guide may help with remembering this down the line:
orange - scarlet - red - crimson - rose - magenta - red-violet
BTW, it's best to avoid referring to crimson as pinkish as this implies it's lighter (as in red tinted with white).
Cheers Chippy, ATM I have the Agincourt scene,Batman (nearly done), Hinchcliffe Gothic Knight, Steve Readdies Pilgrim Knight and this one in various stages of work and a few in the grey army lol