Given Falkenhayn's overall strategy, I don't think attacking the British makes much sense. He'll likely want to bait them into continuing the offensive and taking disproportionate casualties.
As for the French part of the front, he might advance if he sees an opening, but only if it he thinks he can manage without attriting himself too much and if it'll put him in a more advantageous position.
Expecting Germany to commit to a big offensive now would be against the principles on which Falkehnayn operates, given that his strategy was based on the understanding that Germany would not be able to defeat the Entente in a war of movements, and that they would need to destroy their armies before a big advance is possible. He'll gladly forgo territorial advances if it means continuing to chip away units of the enemy armies.
As for the French part of the front, he might advance if he sees an opening, but only if it he thinks he can manage without attriting himself too much and if it'll put him in a more advantageous position.
Expecting Germany to commit to a big offensive now would be against the principles on which Falkehnayn operates, given that his strategy was based on the understanding that Germany would not be able to defeat the Entente in a war of movements, and that they would need to destroy their armies before a big advance is possible. He'll gladly forgo territorial advances if it means continuing to chip away units of the enemy armies.