Update: I misunderstood what was the nature of the prior information. You have a problem with your experiment, because we can't disentangle the effect of the nationality from the effect of the banner. As far as I understood, banner_past is different from banner A and B. So, you know that, on banner-past, french are slightly more likely to click on the banner. Now, since you didn't show banner A to any american, and banner B to any french, how can we estimate the effect of each banner, conditional on the nationality? It can't be done, as far as I can imagine.
Old Answer:
Use Bayes!
For simplicity here, I'll assume the probability of clicking on banner $A$ follows a Binomial distribution with probability $\theta_{a}$ and the probability of clicking on banner $B$ follows a Binomial distribution with probability $\theta_{b}$. You're interested on knowing if $\theta_{a}$ > $\theta_{b}$. If so, you`ll use banner A.
If we assume a conjugated prior for this likelihood, namely, a beta distribution for $\theta_{a}$ with paramaters ($\alpha_{a}$, $\beta_{a}$) and another one with parameters ($\alpha_{b}$, $\beta_{b}$) for $\theta_{b}$, where $\alpha_{a}$ is the number of clicks on banner $A$ and $\beta_{a}$ is the number of people that saw banner $A$ but didn't click on it. The same for banner $B$. You can use prior information on the number of clicks on banner $A$ and on the number of clicks on banner $B$ and compute the posterior probability of $\theta_{a}$ and of $\theta_{b}$. The posteriori will be Beta distributions with parameters ($\alpha_{a}$ + number of clicks on $A$ on the new experiment, $\beta_{a}$ + number of people who saw banner $A$, but didn't click on it on the new experiment) and ($\alpha_{b}$ + number of clicks on $B$ on the new experiment, $\beta_{b}$ + number of people who saw banner $B$, but didn't click on it on the new experiment) for banners $A$ and $B$ respectively. To compute the posterior probability of $\theta_{a}$ - $\theta_{b}$, just run a simulation.
Please note that in this modeling I assumed that you have prior information not only on the 51%, but also on the number of cases that resulted in this 51% number. This is important to weight how much information this 51% really carries on. 51% with say 100 cases is much less informative than 10,000 cases.
Update: Based on your commnet, here's a R code to your question:
set.seed(2)
posterioriA <- rbeta(n_trials, 5100 + 1850, 80000-5100 + 31400-1850 )
posteriorib <- rbeta(n_trials, 4900 + 1950, 80200-4900 + 32000-1950 )
posterioriDifAB <- posterioriA - posteriorib
# probability that banner A is better than Banner B, i.e., it has a higher probability of click
sum(posterioriDifAB > 0)/length(posterioriDifAB)
# in my computer, 0.9063
So, the posterior probability of Banner A being better than banner B is 90%. You can compute, also, the probability that banner A is substantially better, if you're able to define this mathematically. Say, for instance, that a substantive improvement is defined as banner A having a probability of click 0.1 p.p bigger than banner B. To see if this is the case, just compute:
sum(posterioriDifAB > 0.001)/length(posterioriDifAB)
# in my computer, 0.6335
So, based on this, although Banner A is statistically better than banner B, it's not substantially better.