It is a map, and so cartographers would likely refer to it as a thematic map (as opposed to a topographical map). The fact that many statistical diagrams have unique names (e.g. a bar chart, a scatterplot, a dotplot) as opposed to just describing their contents can sometime be a hindrance. Both because not everything is named (as is the case here) and the same name can refer to different types of displays (dotplot is a good example).
In the Grammar of Graphics Wilkinson describes a graph as geometric elements displayed in a particular coordinate system. Here he refers to Napoleon's March as a path element whose width represents the number of troops. In this example the path is drawn in a Cartesian coordinate system whose points represent actual locations in Europe. The points are connected as a representation of the journey Napoleon and his army took, although it likely does not exactly trace the journey (nor does the wider element at the start mean the army took up more space on the road!)
There are many different software programs that have the capabilities to to draw this type of diagram. Michael Friendly has a whole page of examples. Below is a slightly amended example using the ggplot2
package in R (as you requested an example in R), although it could certainly be replicated in base graphics.
mydir <- "your directory here"
setwd(mydir)
library(ggplot2)
troops <- read.table("troops.txt", header=T)
#data is from Friendly link
cities <- read.table("cities.txt", header=T)
#http://www.datavis.ca/gallery/minard/ggplot2/ggplot2-minard-gallery.zip
temps <- read.table("temps.txt", header=T)
temps$date <- as.Date(strptime(temps$date,"%d%b%Y"))
xlim <- scale_x_continuous(limits = c(24, 39))
p <- ggplot(cities, aes(x = long, y = lat)) +
geom_path(
aes(size = survivors, colour = direction, group = group),
data=troops, linejoin = "round", lineend = "round"
) +
geom_point() +
geom_text(aes(label = city), hjust=0, vjust=1, size=4) +
scale_size(range = c(1, 10)) +
scale_colour_manual(values = c("grey50","red")) +
xlim + coord_fixed(ratio = 1)
p
ggsave(file = "march.png", width=16, height=4)

Here are a few of the things that make this different than the original:
- I did not display the temperature graph at the bottom of the plot. In
ggplot2
you can make a separate graph, you cannot draw lines across the separate graph windows though.
- Minard's original graph shows the path diminishing in steps between cities. This graph does not interpolate the losses like that, and shows abrupt changes from city to city. (Troop sizes are taken from a diary of a physician who traveled with the army I believe)
- This graph shows the exact location of the contemporary cities, Minard tended to bend space slightly to make the graph nicer. A more blatant example is the location of England in Minards map of migration flows.