Is genome recurrence possible like in Jupiter Ascending?
Various types of genetic variation exist in natural populations. One is the single-nucleotide polymorphism (SNP), which is where different nucleotides are present at the same location in the genome of different individuals in a population (with variation present in a nontrivial number of people; the threshold is usually set arbitrarily at 1%).

Even just considering SNPs and ignoring other types of variation, what you talk about would be effectively impossible.

The human genome is about 3 billion base-pairs long. Along the whole genome, according to Chen et al 2012, between two individuals there is something like 3 million SNPs. Imagine two people flipping a coin and the result is exactly the same every time, 3 million times. Now imagine instead of heads or tails, there are 4 options. 

Only 1 result of the series of 3 million 1 in 4 chances is identical to the original series.

$\frac{1}{4^{3000000}}\approx\frac{1}{\infty}$ = 0

Go ahead, try it on your calculator.

Now, there are also variations that are beyond SNPs between individuals that cause much more variation between two people. These can cause even more "unprobability". Since we already require infinite people before this event is likely to happen, I think we can just call this event impossible.