I had thought that surcoats didnt exist in the late 11th-early 12th century, but then i came across this paragraph in Gesta Francorum:
'Deferunt arma ad bellum congrua, in dextra uel inter utrasque scapulas crucem Christi baiulant; sonum uero "Deus uult, Deus uult, Deus uult!"

Translation:
"They bear arms suitable for battle; on the right shoulder, or between both shoulders, they wear the cross of Christ; the cry, 'God wills it! God wills it! God wills it!'

So did they have surcoats at this time or was the cross just sown into the mail?

Can someone point me to some other sources where they describe this in more detail, such as the color of the cross, if it was specified rather than left for individual soldiers to decide.

Any sources would be appreciated :)

Gesta Francorum: http://www.thelatinlibrary.com/gestafrancorum...rum1.shtml

Translation:
https://sourcebooks.fordham.edu/source/gesta-cde.asp#endpop

As you said, Joonas, there's no evidence of surcoats at this time. Surcoats are specific garments of clothing that don't appear until right around 1200 AD. However, it was certainly possible for someone to wear a layer of clothing over top of their mail, onto which a cross could be sewn. Alternatively, a cloth cross could be affixed to the mail with a brooch or something similar.

Please keep in mind my ideas about how the cross was attached are just speculation. We can be confident, however, that whatever the crusaders wore at this stage, it was not a surcoat.

"They bear arms suitable for battle"
Now I don't know the text beyond what you posted, but couldn't it also mean that gambesons were worn instead?

In the same liber from the Gesta Francorum, first paragraph, it reads:

Quote:

Franci audientes talia protinus in dextra crucem suere scapula

Which seems to translate in: "hearing this, the Franks immediately sew a cross on their right shoulder". It may also be "rightly have sewn a cross on their shoulder". But "suere" is unmistakenly related with sewing/stitching. It could have been directly on the mail itself, or it could have been on a piece of cloth, like an apron, chasuble or something.

Now on what exactly is based the certainty that they didn't wear anything over their coat? As far as I know, 11th century iconography is relatively scarce, and often badly documented. The main source I'm thinking of are sculptures on column's capitals, and that it is really badly documented (simply because it's difficult to take a good picture from the ground - 11th and 12th century churches interiors are often underlit and quite narrow).

But nowhere it's written they do all this "in armor". The cross might simply be sewn on their "civilian" clothing. It seems "defero" means to bring, to take with, to move, not really to wear, so in the context of the sentence we can't safely assume that the crosses mentioned are on the "arma ad bellum congrua".