To obtain the Falcor glaive you have several options, being the first one to buy it directly through the Market console or the Arsenal for 150 Platinum. If you choose this option, you also get an extra weapon slot as well as an Orokin Catalyst already installed.
On the other side you can also obtain the Falcor Blueprint in the Corpus lab of your Clan´s Dojo. To do that you need to complete the Falcor investigation, contributing with all required resources. This is the traditional way, and also the slowest.