« first day (1 day earlier)      last day (18 days later) » 

AFH
AFH
00:43
The following two lines from the middle of the log seem to to show when things start to go wrong. 
2016-01-07 23:40:52, Info CONX ConX::Compatibility::CSystemAbstraction::HostIsUEFIFirmware: Host is UEFI.
2016-01-07 23:40:52, Error CONX ConX::Compatibility::CSystemAbstraction::HostIsUEFIDiskLayout: Failed to retrieve system partition NT path.
AFH
AFH
00:55
I found a link which suggested that getting rid of grub can cure installations problem, but your question implies that you are not using it.
The link is here. Although it refers to Windows 7, it may be relevant to 8.1.
 
15 hours later…
user2284570
user2284570
15:54
@AFH Yes, the windows bootloader execute winload.efi to start windows. I added an alternate windows installation to the ʙᴄᴅ that use linux-3.16-pf.efi instead of windload.efi. I hard coded the necessary information in the kernel to mount and chroot on my debian partition (/dev/sda6).
Deleting that supplemental entry didn't solved my problem.
And, reagentc fails to enable winre again :

C:\Users\example>reagentc /enable
REAGENTC.EXE : operation failed. b7

REAGENTC.EXE : an error occurred.
user2284570
user2284570
16:13
I could’t found what to do in order to solve the b7 error code.
@AFH This solution is for ᴍʙʀ only.
 
2 hours later…
AFH
AFH
18:17
This link seems to deal with UEFI repair for all disc types. I know you can boot, so your boot loader doesn't need repairing as such, but these instructions may get it into a better state for upgrading to Win10.
 
2 hours later…
user2284570
user2284570
20:13
@AFH I think I finnally found the issue.
DISKPART> list part

N° partition Type Taille Décalage
------------- ---------------- ------- --------
Partition 1 Inconnu 300 M 1024 K
Partition 2 Récupération 100 M 301 M
Partition 4 Réservé 100 M 429 M
Partition 5 Principale 979 G 529 M
Partition 6 Principale 4714 M 980 G
Partition 4 Principale 337 M 985 G
Partition 8 Inconnu 298 G 1028 G
Partition 9 Inconnu 6981 M 1422 G
Where inconnu is the translation of unknow.
So Partition 1 Inconnu 300 M 1024 K

should be

Partition 1 Système 300 M 1024 K

according to this reference image :
user image
It occurs at HostIsUEFIDiskLayout which check if windows have correct partition layout. I think it simply fails to find such partition with the expected ɢᴘᴛ attributes.

However, I have no idea how to set the required ɢᴘᴛ attributes.
with diskpart on Partition 1.
 
2 hours later…
AFH
AFH
22:42
Have you tried bootrec /fixboot? Alternatively, since the tag indicates that your Linux system is Debian, you should have gparted available, and this is able to set the partition flags. The EFI partition has both boot and esp set, and most of the others (including recovery) have msftdata set only, except that the Linux swap partition has no flags. I am not sure how these flags relate to the diskpart report.
user2284570
user2284570
@AFH bootrec /fixboot will delete the huge time I put in bcdedit for executing the linux kernel as an efi application.
In the meantime bootrec don't modify partition types.
AFH
AFH
You can take a copy of just that partition and restore it if the upgrade works. But try gparted first.
 
1 hour later…
user2284570
user2284570
23:57
gparted would never had been able to [solve the problem](http://superuser.com/a/1023752/282033). Please also note partition creation would involve renumbering so deleting and recreating would have prevented windows from booting.
I’ll try this out.

« first day (1 day earlier)      last day (18 days later) »