You need to do some diagnostics but I would read the following post sinc 99% of what your doing is covered in this previous post
Also, i would get ipsec log and diag debug application ike -1 from the linux client and fortigate respectively.
Lastly, you need to do some packet captures on linux ( e.g tcpdump -nnvvv -i eth0 host x.x.x.x and port 500 or 4500 ) or ( fgt. cli. diag sniffer packet any "host y.y.y.y" )
In your cfg I would also simplify the following lines and ensure you have this
right=vpnserverfgt100D.example.com. # the dns or ipv4 address of fortigate interfaces that matches the address in phase1-interface interface rightsubnet=0.0.0.0/0
# optional probably not needed
firstname.lastname@example.org. # I would set a matching IKE-ID on the fortigate and then populate that here in your cfg
ipsec up your "fortinet" profile , grab your logs, grab a packet capture at the linux host and|or fortigate and then do the proper analysis based on your findings.
tip, if you have iptables
you need proper rules to allow traffic.
YMMV but the above examples , link and tips should get you pointed in the right direction.