The signs Virgo and Sagittarius form a square relationship in the zodiac. What this means is that there is always a fundamental strain in the interaction; you might say one of having cross-purposes in life. Still, Virgo and Sagittarius are both mentally oriented signs that communicate well and can relate to each other in an immediate fashion. The problem is that Sagittarius is ever expansive and often naively optimistic, while Virgo has a great need of getting down to details and to the realities of life. Sometimes so much that negativism or fault-finding takes over completely. Yet Sagittarius is a good inspirer, and Virgo is receptive and appreciative of the social ease and naturalness of Sag.
Also, Virgo can direct and administrate the enthusiasm of Sag to the benefit of both. Romantically, things are more complicated. Virgo may be able to give Sagittarius the freedom they need, (Sagittarius typically has a large circle of friends and associates) yet there is something missing. A stable, continuous flow of passion and affection between these two is perhaps unlikely. Instead they could take on roles that somehow presuppose too much about what the partner ought to be, and neither is eager enough in trying to fuel the relationship with that special sort of intimacy that sound love-unions seem to require.