Large-scale multimodal foundation models, particularly Contrastive Captioners (CoCa), have achieved state-of-the-art results by unifying contrastive alignment with generative captioning. While zero-shot transfer capabilities are well-documented, the adaptation of these generative-contrastive hybrids to downstream tasks with extreme data scarcity (few-shot learning) remains under-explored. Existing literature predominantly focuses on dual-encoder architectures like CLIP, leaving a gap in understanding how CoCa's distinct latent space responds to parameter-efficient fine-tuning (PEFT). This paper presents a comprehensive empirical study on adapting the CoCa visual backbone for few-shot image classification. We systematically evaluate a hierarchy of strategies, ranging from training-free hybrid prototyping to deep parameter adaptation via Low-Rank Adaptation (LoRA). First, we identify an "augmentation divergence": while strong data augmentation degrades the performance of linear probing in low-shot settings, it is essential for stabilizing LoRA fine-tuning. We also demonstrate that hybrid objectives incorporating Supervised Contrastive (SupCon) loss yield consistent performance improvements over standard Cross-Entropy across varying shot counts. Crucially, we characterize the sensitivity of training configurations to data scarcity, providing empirical reference settings for scaling regularization, rank, and sampling strategies to facilitate the efficient adaptation of generative-contrastive foundation models.