NP here. In a similar situation, and I did spend some time talking to the principal (previous one) and the district. The expectations for the older grades is that the kid would be fluent enough to be able to contribute in science and math classes, explain his or her thinking, make hypotheses and generally be a contributor in the class. Since KG does partial immersion, and the math and science classes are targeted, there is an emphasis on STEM vocabulary in French. There is no formal exam, just a conversation with a teacher, and there is no formal assessment at the end, other than the grade in the report card.
The lottery is competitive. We tried for 1st grade this year, and ended up at #99. By the beginning of the year, it was down to #53 -- still far from likely that we'd be able to join. A few years before, we tried to gain admission for our eldest child while living inside the boundary. We started the summer at #39, still did not get in, and ended up moving outside the boundaries (we were new to VA back then, deciding where to live).
BTW, The school web site does talk about a 2nd grade lottery, but there is no such mention on the FCPS site.
http://www.fcps.edu/is/worldlanguages/immersion.shtml
Maybe it's something they would consider next year. I would like to hear more about it, as we would still be pursuing admission if it were an option for 2nd grade. Since they have a large school with a large local community of French speakers, the French spots fill quickly, and there are always a long list of siblings waiting to get in. So I would not have high expectations, but who knows? 3rd time's the charm.