Complex sentence: If the local French administrator on occasion decided against them, they would appeal to their political contacts in Paris, whom they carefully cultivated, e.g., the large, political-pressure group "Parti-Colonial".
Split into simpler sentences: If the local French administrator on occasion decided against them, they would hasten to appeal to their political contacts in Paris. These they carefully cultivated, e.g., the large, political pressure group "Parti-Colonial".