This paper presents the prospects for a precise measurement of the branching fraction of the leptonic $$ {B}_c^{+} $$
B
c
+
→ τ+ντ decay at the Future Circular Collider (FCC-ee) running at the Z -pole. A detailed description of the simulation and analysis framework is provided. To select signal candidates, two Boosted Decision Tree algorithms are employed and optimised. The first stage suppresses inclusive $$ b\overline{b} $$
b
b
¯
, $$ c\overline{c} $$
c
c
¯
, and $$ q\overline{q} $$
q
q
¯
backgrounds using event-based topological information. A second stage utilises the properties of the hadronic τ+→ π+π+π−$$ \overline{\nu} $$
ν
¯
τ decay to further suppress these backgrounds, and is also found to achieve high rejection for the B+→ τ+ντ background. The number of $$ {B}_c^{+} $$
B
c
+
→ τ+ντ candidates is estimated for various Tera-Z scenarios, and the potential precision of signal yield and branching fraction measurements evaluated. The phenomenological impact of such measurements on various New Physics scenarios is also explored.