Let me sum up in 1715, to see if I am not mistaken
1. Louis XIV (m. Maria Teresa of Spain)
1.1. Louis, grand dauphin m. Mary of York
1.1.1. Louis, duke of Burgundy (b. 1681)
1.1.2. Charles, duke of Anjou (b. 1684)
1.1.4. James, duke of Berry (b. 1686)
1.1.3. Anne, madame royale (b. 1688)
1.2. (ill.) Louis Auguste, duke of Maine (b. 1670)
1.2. (ill.) Louis César, abbé de Bourbon (b. 1672)
1.3. (ill.) Louise Françoise, mademoiselle de Nantes (b. 1673)
1.4. (ill.) Françoise Marie, mademoiselle de Blois (b. 1677)
1.5. (ill.) Louis Alexandre, count of Toulouse (b. 1678)
2. (Philippe, duke of Orleans)
2.1. Marie Louise, mademoiselle d'Orléans (b. 1662)
2.2. Anne Marie, mademoiselle de Valois (b. 1669)
2.3. Philippe, duke of Orleans (b. 1674)
2.4. Elisabeth Charlotte, mademoiselle d'Orléans (b. 1676) m. James of Cambridge
1. (Charles II)
1.1. Charles III (b. 1669) m. Sophie Charlotte of Hannover
2. James, duke of York m. Anne Hyde m. Claudia Felicitas of Austria-Tyrol
2.1. Mary m. Louis, grand dauphin
2.2. Anne, m. Friedrich, electoral prince of Brandenburg
2.3. Henriette m. Maximilian of Hannover, duke of Cumberland
2.4. James Leopold, duke of Cambridge (b. 1674) m. Elisabeth Charlotte of Orleans
2.5. Isabella (b. 1676) m. Charles of Austria
Given how both Louis XIV and Charles II were fond of their bastards, could not they play a role in the alliance system ?