I'd like to add something to the conversation here -
The following is a traceroute to the NA / EU datacenter in Montreal by an ISP in southeastern Europe (Athens, Greece):
Code:
Non-prime time (23:50 BST - 01:50 EET)
Tracing route to 199.91.189.25 over a maximum of 30 hops
1 1 ms 1 ms 1 ms dsldevice.lan [192.168.1.1]
2 25 ms 24 ms 24 ms bbras-llu-kln-15L500.forthnet.gr [213.16.246.12]
3 25 ms 24 ms 25 ms 213.16.247.73
4 28 ms 28 ms 26 ms core-kln-12Be3.forthnet.gr [213.16.247.17]
5 25 ms 27 ms 28 ms te-3-2.car1.Sofia2.Level3.net [212.162.46.109]
6 65 ms 68 ms 65 ms 4.69.141.109
7 71 ms 76 ms 73 ms ae-10-10.ebr3.Frankfurt1.Level3.net [4.69.141.34]
8 66 ms 66 ms 66 ms ae-73-73.csw2.Frankfurt1.Level3.net [4.69.163.6]
9 66 ms 66 ms 65 ms ae-2-70.edge4.Frankfurt1.Level3.net [4.69.154.72]
10 77 ms 78 ms 78 ms 4.68.111.146
11 157 ms 156 ms 157 ms if-7-2.tcore1.FNM-Frankfurt.as6453.net [195.219.50.2]
12 156 ms 155 ms 156 ms if-5-2.tcore1.AV2-Amsterdam.as6453.net [195.219.194.13]
13 163 ms 160 ms 159 ms if-2-2.tcore2.AV2-Amsterdam.as6453.net [195.219.194.6]
14 173 ms 171 ms 172 ms if-7-2.tcore2.L78-London.as6453.net [80.231.152.14]
15 158 ms 159 ms 158 ms if-20-2.tcore2.NYY-NewYork.as6453.net [216.6.99.13]
16 156 ms 157 ms 155 ms if-2-2.tcore2.MTT-Montreal.as6453.net [64.86.226.13]
17 158 ms 158 ms 166 ms if-0-2.tcore1.MTT-Montreal.as6453.net [216.6.115.89]
18 159 ms 161 ms 157 ms if-5-2.tcore1.W6C-Montreal.as6453.net [64.86.31.6]
19 164 ms 164 ms 163 ms 66.198.96.50
20 166 ms 166 ms 170 ms 192.34.76.2
21 182 ms 183 ms 183 ms 199.91.189.234
22 166 ms 165 ms 165 ms 199.91.189.25
Trace complete.
Code:
Prime time (19:00 BST - 21:00 EET)
1 1 ms 2 ms 1 ms 192.168.1.1
2 23 ms 22 ms 22 ms bbras-llu-kln-15L500.forthnet.gr [213.16.246.12]
3 23 ms 22 ms 22 ms 213.16.247.73
4 25 ms 23 ms 23 ms core-kln-12Be3.forthnet.gr [213.16.247.17]
5 33 ms 35 ms 33 ms te-3-2.car1.Sofia2.Level3.net [212.162.46.109]
6 63 ms 63 ms 62 ms 4.69.141.109
7 63 ms 67 ms 74 ms ae-10-10.ebr3.Frankfurt1.Level3.net [4.69.141.34]
8 64 ms 63 ms 63 ms ae-93-93.csw4.Frankfurt1.Level3.net [4.69.163.14]
9 64 ms 63 ms 63 ms ae-4-90.edge4.Frankfurt1.Level3.net [4.69.154.200]
10 62 ms 61 ms 62 ms 4.68.111.146
11 158 ms 158 ms 159 ms if-4-2.tcore1.PVU-Paris.as6453.net [80.231.153.10]
12 298 ms 306 ms 319 ms if-2-2.tcore1.PYE-Paris.as6453.net [80.231.154.18]
13 332 ms 328 ms 325 ms if-5-2.tcore1.L78-London.as6453.net [80.231.130.1]
14 333 ms 316 ms 338 ms if-1-2.tcore2.L78-London.as6453.net [80.231.130.122]
15 314 ms 305 ms 303 ms if-20-2.tcore2.NYY-NewYork.as6453.net [216.6.99.13]
16 325 ms 328 ms 345 ms if-5-2.tcore2.MTT-Montreal.as6453.net [216.6.99.30]
17 332 ms 315 ms 308 ms if-0-2.tcore1.MTT-Montreal.as6453.net [216.6.115.89]
18 315 ms 329 ms 342 ms if-5-2.tcore1.W6C-Montreal.as6453.net [64.86.31.6]
19 319 ms 324 ms 317 ms 66.198.96.50
20 336 ms 327 ms 316 ms 192.34.76.2
21 316 ms 312 ms 305 ms 199.91.189.234
22 322 ms 318 ms 321 ms 199.91.189.25
Okay. I have submitted these traceroutes to them, via support (and for the first one, which was in the initial ticket, they mercifully said they'd "forward it to the datacenter", something I honestly did not expect, despite being very rational to do so).
I have also told them the following, in an e-mail response:
You will notice that the 300+ ms in Paris or London (in bold above) are over what they should be (Europe-to-Europe connectivity should be at 100 ms or less, as you can see Athens-Frankfurt is "only" 63).
Since after Paris, the rest of the route up to Montreal is entirely within TATA (London, New York, and finally Montreal), I presume that TATA must be the primary / only provider of bandwidth for your Montreal datacenter.
So, it would be wise for Square Enix to take this up with them (TATA). Perhaps they can perform network upgrades or otherwise direct traffic from / to your Montreal datacenter through links which are less congested.
TL;DR: Square Enix / EIDOS Montreal should take up this issue with TATA, to alleviate problems with EU players in general, since the problem is not isolated or restricted to few cases only. It appears that a significant discrepancy exists in "prime time" hours, when links are severely congested and produce double the pings + packet loss, hence normal gameplay under these conditions is totally unfeasible.
Alternatively, Square Enix could decide to deploy some servers in UK, where Square Enix Europe is, and automatically stop worrying about TATA links 
Conclusion
I hope you understood the issue from a networking POV, at least as adequately as simple testing can allow this to be done. There are more elaborate ways to test, however, the link congestion will not go away on its own, unless Eidos Montreal decides to significantly change their Internet bandwidth providers and / or take this up with TATA which seems to be the only ones taking EU players to them as things are.