I'm afraid there are some ... inaccuracies I would like to adress.
...
Tropical West Africa's an awful place for Europeans to fight a war,
...
Only that Cameroon sports the "wet" tropical region only in its most southern parts.
The bulk of Cameroon was and is a rather dry, savannah-like country as
might be seen here.
Would the French be able to easily march into Cameroon and Togoland?
Its exactly what they did OTL so yes
Well ...
exactly? ... No
In Togo as well as Cameroon the french did not invade alone but together with the Brits who - in both cases - concentrated on the most developed coastal regions first, while the french esp. in Cameroon taking different approaches.
However, without the Brits the germans in Togo would have outnumbered their french counterparts even in 'european' soldiers alone. Without having to fight a 2-front war as IOTL they would have kept the french in check for much longer, if not even counterattacked into French-Dahomey. Though I admit that France - with some time - would be able to reinforce (though questionable if they would make the effort).
Regarding the problem of a 2-front war the same would count for Cameroon : the germans now won't have to fight Brits and french. And despite the numerical superiority of the french alone in this theatre the germans managed IOTL to hold their stance until 1916 with even counterattacking several time.
Again I would asume that without the Brits the germans might inflict much more ... problem to the french than IOTL.
Also : what would happen to the SMS Königsberg ?
IOTL she was ... 'caught' in East-Africa with her task attacking the entrance of the Red Sea.
Something that might not be necessary (Britain ins't in yet) ITTL.
It that might have been used to support the german colonies against the remaining enemy on the continent France ... aka sailing to the Gulf of Guinea.
Last but not least ... without the british control of the seas the supply situation for the german colonial troops would be much better.
Therefore the french might try to invade Togo and Cameroon by themself, but would have some rather hard time with rather uncertain outcomes, at least with much longer fighting than IOTL